diff --git a/compiler/rustc_hir_analysis/src/coherence/inherent_impls.rs b/compiler/rustc_hir_analysis/src/coherence/inherent_impls.rs
index e2d3ff558cf7d..8d0e8818162ad 100644
--- a/compiler/rustc_hir_analysis/src/coherence/inherent_impls.rs
+++ b/compiler/rustc_hir_analysis/src/coherence/inherent_impls.rs
@@ -90,7 +90,8 @@ impl<'tcx> InherentCollect<'tcx> {
                 }
             }
 
-            if let Some(simp) = simplify_type(self.tcx, self_ty, TreatParams::AsCandidateKey) {
+            if let Some(simp) = simplify_type(self.tcx, self_ty, TreatParams::InstantiateWithInfer)
+            {
                 self.impls_map.incoherent_impls.entry(simp).or_default().push(impl_def_id);
             } else {
                 bug!("unexpected self type: {:?}", self_ty);
@@ -129,7 +130,7 @@ impl<'tcx> InherentCollect<'tcx> {
             }
         }
 
-        if let Some(simp) = simplify_type(self.tcx, ty, TreatParams::AsCandidateKey) {
+        if let Some(simp) = simplify_type(self.tcx, ty, TreatParams::InstantiateWithInfer) {
             self.impls_map.incoherent_impls.entry(simp).or_default().push(impl_def_id);
         } else {
             bug!("unexpected primitive type: {:?}", ty);
diff --git a/compiler/rustc_hir_typeck/src/method/probe.rs b/compiler/rustc_hir_typeck/src/method/probe.rs
index 28f537c87c4ee..a566759091209 100644
--- a/compiler/rustc_hir_typeck/src/method/probe.rs
+++ b/compiler/rustc_hir_typeck/src/method/probe.rs
@@ -714,7 +714,7 @@ impl<'a, 'tcx> ProbeContext<'a, 'tcx> {
     }
 
     fn assemble_inherent_candidates_for_incoherent_ty(&mut self, self_ty: Ty<'tcx>) {
-        let Some(simp) = simplify_type(self.tcx, self_ty, TreatParams::AsCandidateKey) else {
+        let Some(simp) = simplify_type(self.tcx, self_ty, TreatParams::InstantiateWithInfer) else {
             bug!("unexpected incoherent type: {:?}", self_ty)
         };
         for &impl_def_id in self.tcx.incoherent_impls(simp).into_iter().flatten() {
diff --git a/compiler/rustc_hir_typeck/src/method/suggest.rs b/compiler/rustc_hir_typeck/src/method/suggest.rs
index 61287d98676b2..9a275a66c52cb 100644
--- a/compiler/rustc_hir_typeck/src/method/suggest.rs
+++ b/compiler/rustc_hir_typeck/src/method/suggest.rs
@@ -2234,8 +2234,12 @@ impl<'a, 'tcx> FnCtxt<'a, 'tcx> {
             let target_ty = self
                 .autoderef(sugg_span, rcvr_ty)
                 .find(|(rcvr_ty, _)| {
-                    DeepRejectCtxt::new(self.tcx, TreatParams::ForLookup)
-                        .types_may_unify(*rcvr_ty, impl_ty)
+                    DeepRejectCtxt::new(
+                        self.tcx,
+                        TreatParams::AsRigid,
+                        TreatParams::InstantiateWithInfer,
+                    )
+                    .types_may_unify(*rcvr_ty, impl_ty)
                 })
                 .map_or(impl_ty, |(ty, _)| ty)
                 .peel_refs();
@@ -2497,7 +2501,7 @@ impl<'a, 'tcx> FnCtxt<'a, 'tcx> {
             .into_iter()
             .any(|info| self.associated_value(info.def_id, item_name).is_some());
         let found_assoc = |ty: Ty<'tcx>| {
-            simplify_type(tcx, ty, TreatParams::AsCandidateKey)
+            simplify_type(tcx, ty, TreatParams::InstantiateWithInfer)
                 .and_then(|simp| {
                     tcx.incoherent_impls(simp)
                         .into_iter()
@@ -3927,7 +3931,7 @@ impl<'a, 'tcx> FnCtxt<'a, 'tcx> {
                 // cases where a positive bound implies a negative impl.
                 (candidates, Vec::new())
             } else if let Some(simp_rcvr_ty) =
-                simplify_type(self.tcx, rcvr_ty, TreatParams::ForLookup)
+                simplify_type(self.tcx, rcvr_ty, TreatParams::AsRigid)
             {
                 let mut potential_candidates = Vec::new();
                 let mut explicitly_negative = Vec::new();
@@ -3945,7 +3949,7 @@ impl<'a, 'tcx> FnCtxt<'a, 'tcx> {
                         .any(|header| {
                             let imp = header.trait_ref.instantiate_identity();
                             let imp_simp =
-                                simplify_type(self.tcx, imp.self_ty(), TreatParams::ForLookup);
+                                simplify_type(self.tcx, imp.self_ty(), TreatParams::AsRigid);
                             imp_simp.is_some_and(|s| s == simp_rcvr_ty)
                         })
                     {
diff --git a/compiler/rustc_metadata/src/rmeta/encoder.rs b/compiler/rustc_metadata/src/rmeta/encoder.rs
index 0d83f8c6c5c93..f8128e988e257 100644
--- a/compiler/rustc_metadata/src/rmeta/encoder.rs
+++ b/compiler/rustc_metadata/src/rmeta/encoder.rs
@@ -2017,7 +2017,7 @@ impl<'a, 'tcx> EncodeContext<'a, 'tcx> {
                 let simplified_self_ty = fast_reject::simplify_type(
                     self.tcx,
                     trait_ref.self_ty(),
-                    TreatParams::AsCandidateKey,
+                    TreatParams::InstantiateWithInfer,
                 );
                 trait_impls
                     .entry(trait_ref.def_id)
diff --git a/compiler/rustc_middle/src/ty/context.rs b/compiler/rustc_middle/src/ty/context.rs
index 971e51be25644..7d8bed789b61e 100644
--- a/compiler/rustc_middle/src/ty/context.rs
+++ b/compiler/rustc_middle/src/ty/context.rs
@@ -437,7 +437,7 @@ impl<'tcx> Interner for TyCtxt<'tcx> {
                 let simp = ty::fast_reject::simplify_type(
                     tcx,
                     self_ty,
-                    ty::fast_reject::TreatParams::ForLookup,
+                    ty::fast_reject::TreatParams::AsRigid,
                 )
                 .unwrap();
                 consider_impls_for_simplified_type(simp);
diff --git a/compiler/rustc_middle/src/ty/trait_def.rs b/compiler/rustc_middle/src/ty/trait_def.rs
index dfb137f738f1e..82690f70e5f18 100644
--- a/compiler/rustc_middle/src/ty/trait_def.rs
+++ b/compiler/rustc_middle/src/ty/trait_def.rs
@@ -168,9 +168,9 @@ impl<'tcx> TyCtxt<'tcx> {
         // whose outer level is not a parameter or projection. Especially for things like
         // `T: Clone` this is incredibly useful as we would otherwise look at all the impls
         // of `Clone` for `Option<T>`, `Vec<T>`, `ConcreteType` and so on.
-        // Note that we're using `TreatParams::ForLookup` to query `non_blanket_impls` while using
-        // `TreatParams::AsCandidateKey` while actually adding them.
-        if let Some(simp) = fast_reject::simplify_type(self, self_ty, TreatParams::ForLookup) {
+        // Note that we're using `TreatParams::AsRigid` to query `non_blanket_impls` while using
+        // `TreatParams::InstantiateWithInfer` while actually adding them.
+        if let Some(simp) = fast_reject::simplify_type(self, self_ty, TreatParams::AsRigid) {
             if let Some(impls) = impls.non_blanket_impls.get(&simp) {
                 for &impl_def_id in impls {
                     f(impl_def_id);
@@ -190,7 +190,9 @@ impl<'tcx> TyCtxt<'tcx> {
         self_ty: Ty<'tcx>,
     ) -> impl Iterator<Item = DefId> + 'tcx {
         let impls = self.trait_impls_of(trait_def_id);
-        if let Some(simp) = fast_reject::simplify_type(self, self_ty, TreatParams::AsCandidateKey) {
+        if let Some(simp) =
+            fast_reject::simplify_type(self, self_ty, TreatParams::InstantiateWithInfer)
+        {
             if let Some(impls) = impls.non_blanket_impls.get(&simp) {
                 return impls.iter().copied();
             }
@@ -239,7 +241,7 @@ pub(super) fn trait_impls_of_provider(tcx: TyCtxt<'_>, trait_id: DefId) -> Trait
         let impl_self_ty = tcx.type_of(impl_def_id).instantiate_identity();
 
         if let Some(simplified_self_ty) =
-            fast_reject::simplify_type(tcx, impl_self_ty, TreatParams::AsCandidateKey)
+            fast_reject::simplify_type(tcx, impl_self_ty, TreatParams::InstantiateWithInfer)
         {
             impls.non_blanket_impls.entry(simplified_self_ty).or_default().push(impl_def_id);
         } else {
diff --git a/compiler/rustc_next_trait_solver/src/solve/normalizes_to/mod.rs b/compiler/rustc_next_trait_solver/src/solve/normalizes_to/mod.rs
index 5738173c7a804..861f032e268dc 100644
--- a/compiler/rustc_next_trait_solver/src/solve/normalizes_to/mod.rs
+++ b/compiler/rustc_next_trait_solver/src/solve/normalizes_to/mod.rs
@@ -144,10 +144,12 @@ where
 
         let goal_trait_ref = goal.predicate.alias.trait_ref(cx);
         let impl_trait_ref = cx.impl_trait_ref(impl_def_id);
-        if !DeepRejectCtxt::new(ecx.cx(), TreatParams::ForLookup).args_may_unify(
-            goal.predicate.alias.trait_ref(cx).args,
-            impl_trait_ref.skip_binder().args,
-        ) {
+        if !DeepRejectCtxt::new(ecx.cx(), TreatParams::AsRigid, TreatParams::InstantiateWithInfer)
+            .args_may_unify(
+                goal.predicate.alias.trait_ref(cx).args,
+                impl_trait_ref.skip_binder().args,
+            )
+        {
             return Err(NoSolution);
         }
 
diff --git a/compiler/rustc_next_trait_solver/src/solve/trait_goals.rs b/compiler/rustc_next_trait_solver/src/solve/trait_goals.rs
index b1dba712f797a..e46c0dd1e3eb1 100644
--- a/compiler/rustc_next_trait_solver/src/solve/trait_goals.rs
+++ b/compiler/rustc_next_trait_solver/src/solve/trait_goals.rs
@@ -47,7 +47,7 @@ where
         let cx = ecx.cx();
 
         let impl_trait_ref = cx.impl_trait_ref(impl_def_id);
-        if !DeepRejectCtxt::new(ecx.cx(), TreatParams::ForLookup)
+        if !DeepRejectCtxt::new(ecx.cx(), TreatParams::AsRigid, TreatParams::InstantiateWithInfer)
             .args_may_unify(goal.predicate.trait_ref.args, impl_trait_ref.skip_binder().args)
         {
             return Err(NoSolution);
diff --git a/compiler/rustc_trait_selection/src/traits/coherence.rs b/compiler/rustc_trait_selection/src/traits/coherence.rs
index 2d843d8f17406..61a1b26132f53 100644
--- a/compiler/rustc_trait_selection/src/traits/coherence.rs
+++ b/compiler/rustc_trait_selection/src/traits/coherence.rs
@@ -94,7 +94,11 @@ pub fn overlapping_impls(
     // Before doing expensive operations like entering an inference context, do
     // a quick check via fast_reject to tell if the impl headers could possibly
     // unify.
-    let drcx = DeepRejectCtxt::new(tcx, TreatParams::AsCandidateKey);
+    let drcx = DeepRejectCtxt::new(
+        tcx,
+        TreatParams::InstantiateWithInfer,
+        TreatParams::InstantiateWithInfer,
+    );
     let impl1_ref = tcx.impl_trait_ref(impl1_def_id);
     let impl2_ref = tcx.impl_trait_ref(impl2_def_id);
     let may_overlap = match (impl1_ref, impl2_ref) {
diff --git a/compiler/rustc_trait_selection/src/traits/select/candidate_assembly.rs b/compiler/rustc_trait_selection/src/traits/select/candidate_assembly.rs
index 9de62031311b7..b78f023a3b43b 100644
--- a/compiler/rustc_trait_selection/src/traits/select/candidate_assembly.rs
+++ b/compiler/rustc_trait_selection/src/traits/select/candidate_assembly.rs
@@ -580,7 +580,11 @@ impl<'cx, 'tcx> SelectionContext<'cx, 'tcx> {
             return;
         }
 
-        let drcx = DeepRejectCtxt::new(self.tcx(), TreatParams::ForLookup);
+        let drcx = DeepRejectCtxt::new(
+            self.tcx(),
+            TreatParams::AsRigid,
+            TreatParams::InstantiateWithInfer,
+        );
         let obligation_args = obligation.predicate.skip_binder().trait_ref.args;
         self.tcx().for_each_relevant_impl(
             obligation.predicate.def_id(),
diff --git a/compiler/rustc_trait_selection/src/traits/specialize/specialization_graph.rs b/compiler/rustc_trait_selection/src/traits/specialize/specialization_graph.rs
index 732f1b0a3d7cc..c0a712cbf9fd8 100644
--- a/compiler/rustc_trait_selection/src/traits/specialize/specialization_graph.rs
+++ b/compiler/rustc_trait_selection/src/traits/specialize/specialization_graph.rs
@@ -40,7 +40,7 @@ impl<'tcx> Children {
     fn insert_blindly(&mut self, tcx: TyCtxt<'tcx>, impl_def_id: DefId) {
         let trait_ref = tcx.impl_trait_ref(impl_def_id).unwrap().skip_binder();
         if let Some(st) =
-            fast_reject::simplify_type(tcx, trait_ref.self_ty(), TreatParams::AsCandidateKey)
+            fast_reject::simplify_type(tcx, trait_ref.self_ty(), TreatParams::InstantiateWithInfer)
         {
             debug!("insert_blindly: impl_def_id={:?} st={:?}", impl_def_id, st);
             self.non_blanket_impls.entry(st).or_default().push(impl_def_id)
@@ -57,7 +57,7 @@ impl<'tcx> Children {
         let trait_ref = tcx.impl_trait_ref(impl_def_id).unwrap().skip_binder();
         let vec: &mut Vec<DefId>;
         if let Some(st) =
-            fast_reject::simplify_type(tcx, trait_ref.self_ty(), TreatParams::AsCandidateKey)
+            fast_reject::simplify_type(tcx, trait_ref.self_ty(), TreatParams::InstantiateWithInfer)
         {
             debug!("remove_existing: impl_def_id={:?} st={:?}", impl_def_id, st);
             vec = self.non_blanket_impls.get_mut(&st).unwrap();
@@ -278,7 +278,7 @@ impl<'tcx> Graph {
         let mut parent = trait_def_id;
         let mut last_lint = None;
         let simplified =
-            fast_reject::simplify_type(tcx, trait_ref.self_ty(), TreatParams::AsCandidateKey);
+            fast_reject::simplify_type(tcx, trait_ref.self_ty(), TreatParams::InstantiateWithInfer);
 
         // Descend the specialization tree, where `parent` is the current parent node.
         loop {
diff --git a/compiler/rustc_type_ir/src/fast_reject.rs b/compiler/rustc_type_ir/src/fast_reject.rs
index 456accd1a1b78..f552ec10d5b56 100644
--- a/compiler/rustc_type_ir/src/fast_reject.rs
+++ b/compiler/rustc_type_ir/src/fast_reject.rs
@@ -74,13 +74,13 @@ impl<HCX: Clone, DefId: HashStable<HCX>> ToStableHashKey<HCX> for SimplifiedType
 pub enum TreatParams {
     /// Treat parameters as infer vars. This is the correct mode for caching
     /// an impl's type for lookup.
-    AsCandidateKey,
+    InstantiateWithInfer,
     /// Treat parameters as placeholders in the given environment. This is the
     /// correct mode for *lookup*, as during candidate selection.
     ///
     /// This also treats projections with inference variables as infer vars
     /// since they could be further normalized.
-    ForLookup,
+    AsRigid,
 }
 
 /// Tries to simplify a type by only returning the outermost injective¹ layer, if one exists.
@@ -138,18 +138,16 @@ pub fn simplify_type<I: Interner>(
         ty::FnPtr(f) => Some(SimplifiedType::Function(f.skip_binder().inputs().len())),
         ty::Placeholder(..) => Some(SimplifiedType::Placeholder),
         ty::Param(_) => match treat_params {
-            TreatParams::ForLookup => Some(SimplifiedType::Placeholder),
-            TreatParams::AsCandidateKey => None,
+            TreatParams::AsRigid => Some(SimplifiedType::Placeholder),
+            TreatParams::InstantiateWithInfer => None,
         },
         ty::Alias(..) => match treat_params {
             // When treating `ty::Param` as a placeholder, projections also
             // don't unify with anything else as long as they are fully normalized.
             // FIXME(-Znext-solver): Can remove this `if` and always simplify to `Placeholder`
             // when the new solver is enabled by default.
-            TreatParams::ForLookup if !ty.has_non_region_infer() => {
-                Some(SimplifiedType::Placeholder)
-            }
-            TreatParams::ForLookup | TreatParams::AsCandidateKey => None,
+            TreatParams::AsRigid if !ty.has_non_region_infer() => Some(SimplifiedType::Placeholder),
+            TreatParams::AsRigid | TreatParams::InstantiateWithInfer => None,
         },
         ty::Foreign(def_id) => Some(SimplifiedType::Foreign(def_id)),
         ty::Error(_) => Some(SimplifiedType::Error),
@@ -171,27 +169,26 @@ impl<DefId> SimplifiedType<DefId> {
     }
 }
 
-/// Given generic arguments from an obligation and an impl,
-/// could these two be unified after replacing parameters in the
-/// the impl with inference variables.
+/// Given generic arguments, could they be unified after
+/// replacing parameters with inference variables or placeholders.
+/// This behavior is toggled using the `TreatParams` fields.
 ///
-/// For obligations, parameters won't be replaced by inference
-/// variables and only unify with themselves. We treat them
-/// the same way we treat placeholders.
+/// We use this to quickly reject impl/wc candidates without needing
+/// to instantiate generic arguments/having to enter a probe.
 ///
 /// We also use this function during coherence. For coherence the
 /// impls only have to overlap for some value, so we treat parameters
-/// on both sides like inference variables. This behavior is toggled
-/// using the `treat_obligation_params` field.
+/// on both sides like inference variables.
 #[derive(Debug, Clone, Copy)]
 pub struct DeepRejectCtxt<I: Interner> {
-    treat_obligation_params: TreatParams,
+    treat_lhs_params: TreatParams,
+    treat_rhs_params: TreatParams,
     _interner: PhantomData<I>,
 }
 
 impl<I: Interner> DeepRejectCtxt<I> {
-    pub fn new(_interner: I, treat_obligation_params: TreatParams) -> Self {
-        DeepRejectCtxt { treat_obligation_params, _interner: PhantomData }
+    pub fn new(_interner: I, treat_lhs_params: TreatParams, treat_rhs_params: TreatParams) -> Self {
+        DeepRejectCtxt { treat_lhs_params, treat_rhs_params, _interner: PhantomData }
     }
 
     pub fn args_may_unify(
@@ -214,184 +211,185 @@ impl<I: Interner> DeepRejectCtxt<I> {
         })
     }
 
-    pub fn types_may_unify(self, obligation_ty: I::Ty, impl_ty: I::Ty) -> bool {
-        match impl_ty.kind() {
-            // Start by checking whether the type in the impl may unify with
-            // pretty much everything. Just return `true` in that case.
-            ty::Param(_) | ty::Error(_) | ty::Alias(..) => return true,
-            // These types only unify with inference variables or their own
-            // variant.
-            ty::Bool
-            | ty::Char
-            | ty::Int(_)
-            | ty::Uint(_)
-            | ty::Float(_)
-            | ty::Adt(..)
-            | ty::Str
-            | ty::Array(..)
-            | ty::Slice(..)
-            | ty::RawPtr(..)
-            | ty::Dynamic(..)
-            | ty::Pat(..)
-            | ty::Ref(..)
-            | ty::Never
-            | ty::Tuple(..)
-            | ty::FnPtr(..)
-            | ty::Foreign(..) => debug_assert!(impl_ty.is_known_rigid()),
-            ty::FnDef(..)
-            | ty::Closure(..)
-            | ty::CoroutineClosure(..)
-            | ty::Coroutine(..)
-            | ty::CoroutineWitness(..)
-            | ty::Placeholder(..)
-            | ty::Bound(..)
-            | ty::Infer(_) => panic!("unexpected impl_ty: {impl_ty:?}"),
-        }
+    pub fn types_may_unify(self, lhs: I::Ty, rhs: I::Ty) -> bool {
+        match (lhs.kind(), rhs.kind()) {
+            (ty::Error(_), _) | (_, ty::Error(_)) => true,
 
-        let k = impl_ty.kind();
-        match obligation_ty.kind() {
-            // Purely rigid types, use structural equivalence.
-            ty::Bool
-            | ty::Char
-            | ty::Int(_)
-            | ty::Uint(_)
-            | ty::Float(_)
-            | ty::Str
-            | ty::Never
-            | ty::Foreign(_) => obligation_ty == impl_ty,
-            ty::Ref(_, obl_ty, obl_mutbl) => match k {
-                ty::Ref(_, impl_ty, impl_mutbl) => {
-                    obl_mutbl == impl_mutbl && self.types_may_unify(obl_ty, impl_ty)
-                }
-                _ => false,
-            },
-            ty::Adt(obl_def, obl_args) => match k {
-                ty::Adt(impl_def, impl_args) => {
-                    obl_def == impl_def && self.args_may_unify(obl_args, impl_args)
-                }
-                _ => false,
-            },
-            ty::Pat(obl_ty, _) => {
-                // FIXME(pattern_types): take pattern into account
-                matches!(k, ty::Pat(impl_ty, _) if self.types_may_unify(obl_ty, impl_ty))
-            }
-            ty::Slice(obl_ty) => {
-                matches!(k, ty::Slice(impl_ty) if self.types_may_unify(obl_ty, impl_ty))
-            }
-            ty::Array(obl_ty, obl_len) => match k {
-                ty::Array(impl_ty, impl_len) => {
-                    self.types_may_unify(obl_ty, impl_ty)
-                        && self.consts_may_unify(obl_len, impl_len)
-                }
-                _ => false,
-            },
-            ty::Tuple(obl) => match k {
-                ty::Tuple(imp) => {
-                    obl.len() == imp.len()
-                        && iter::zip(obl.iter(), imp.iter())
-                            .all(|(obl, imp)| self.types_may_unify(obl, imp))
-                }
-                _ => false,
-            },
-            ty::RawPtr(obl_ty, obl_mutbl) => match k {
-                ty::RawPtr(imp_ty, imp_mutbl) => {
-                    obl_mutbl == imp_mutbl && self.types_may_unify(obl_ty, imp_ty)
+            // As we're walking the whole type, it may encounter projections
+            // inside of binders and what not, so we're just going to assume that
+            // projections can unify with other stuff.
+            //
+            // Looking forward to lazy normalization this is the safer strategy anyways.
+            (ty::Alias(..), _) | (_, ty::Alias(..)) => true,
+
+            // Bound type variables may unify with rigid types e.g. when using
+            // non-lifetime binders.
+            (ty::Bound(..), _) | (_, ty::Bound(..)) => true,
+
+            (ty::Infer(var), _) => self.var_and_ty_may_unify(var, rhs),
+            (_, ty::Infer(var)) => self.var_and_ty_may_unify(var, lhs),
+
+            (ty::Param(lhs), ty::Param(rhs)) => {
+                match (self.treat_lhs_params, self.treat_rhs_params) {
+                    (TreatParams::AsRigid, TreatParams::AsRigid) => lhs == rhs,
+                    (TreatParams::InstantiateWithInfer, _)
+                    | (_, TreatParams::InstantiateWithInfer) => true,
                 }
-                _ => false,
-            },
-            ty::Dynamic(obl_preds, ..) => {
-                // Ideally we would walk the existential predicates here or at least
-                // compare their length. But considering that the relevant `Relate` impl
-                // actually sorts and deduplicates these, that doesn't work.
-                matches!(k, ty::Dynamic(impl_preds, ..) if
-                    obl_preds.principal_def_id() == impl_preds.principal_def_id()
-                )
             }
-            ty::FnPtr(obl_sig) => match k {
-                ty::FnPtr(impl_sig) => {
-                    let ty::FnSig { inputs_and_output, c_variadic, safety, abi } =
-                        obl_sig.skip_binder();
-                    let impl_sig = impl_sig.skip_binder();
-
-                    abi == impl_sig.abi
-                        && c_variadic == impl_sig.c_variadic
-                        && safety == impl_sig.safety
-                        && inputs_and_output.len() == impl_sig.inputs_and_output.len()
-                        && iter::zip(inputs_and_output.iter(), impl_sig.inputs_and_output.iter())
-                            .all(|(obl, imp)| self.types_may_unify(obl, imp))
-                }
-                _ => false,
-            },
+            (ty::Param(_), _) => self.treat_lhs_params == TreatParams::InstantiateWithInfer,
+            (_, ty::Param(_)) => self.treat_rhs_params == TreatParams::InstantiateWithInfer,
 
-            // Impls cannot contain these types as these cannot be named directly.
-            ty::FnDef(..) | ty::Closure(..) | ty::CoroutineClosure(..) | ty::Coroutine(..) => false,
+            // Placeholder types don't unify with anything on their own.
+            (ty::Placeholder(lhs), ty::Placeholder(rhs)) => lhs == rhs,
 
-            // Placeholder types don't unify with anything on their own
-            ty::Placeholder(..) | ty::Bound(..) => false,
+            // Purely rigid types, use structural equivalence.
+            (ty::Bool, ty::Bool)
+            | (ty::Char, ty::Char)
+            | (ty::Int(_), ty::Int(_))
+            | (ty::Uint(_), ty::Uint(_))
+            | (ty::Float(_), ty::Float(_))
+            | (ty::Str, ty::Str)
+            | (ty::Never, ty::Never)
+            | (ty::Foreign(_), ty::Foreign(_)) => lhs == rhs,
 
-            // Depending on the value of `treat_obligation_params`, we either
-            // treat generic parameters like placeholders or like inference variables.
-            ty::Param(_) => match self.treat_obligation_params {
-                TreatParams::ForLookup => false,
-                TreatParams::AsCandidateKey => true,
-            },
+            (ty::Ref(_, lhs_ty, lhs_mutbl), ty::Ref(_, rhs_ty, rhs_mutbl)) => {
+                lhs_mutbl == rhs_mutbl && self.types_may_unify(lhs_ty, rhs_ty)
+            }
 
-            ty::Infer(ty::IntVar(_)) => impl_ty.is_integral(),
+            (ty::Adt(lhs_def, lhs_args), ty::Adt(rhs_def, rhs_args)) => {
+                lhs_def == rhs_def && self.args_may_unify(lhs_args, rhs_args)
+            }
 
-            ty::Infer(ty::FloatVar(_)) => impl_ty.is_floating_point(),
+            (ty::Pat(lhs_ty, _), ty::Pat(rhs_ty, _)) => {
+                // FIXME(pattern_types): take pattern into account
+                self.types_may_unify(lhs_ty, rhs_ty)
+            }
 
-            ty::Infer(_) => true,
+            (ty::Slice(lhs_ty), ty::Slice(rhs_ty)) => self.types_may_unify(lhs_ty, rhs_ty),
 
-            // As we're walking the whole type, it may encounter projections
-            // inside of binders and what not, so we're just going to assume that
-            // projections can unify with other stuff.
-            //
-            // Looking forward to lazy normalization this is the safer strategy anyways.
-            ty::Alias(..) => true,
+            (ty::Array(lhs_ty, lhs_len), ty::Array(rhs_ty, rhs_len)) => {
+                self.types_may_unify(lhs_ty, rhs_ty) && self.consts_may_unify(lhs_len, rhs_len)
+            }
 
-            ty::Error(_) => true,
+            (ty::Tuple(lhs), ty::Tuple(rhs)) => {
+                lhs.len() == rhs.len()
+                    && iter::zip(lhs.iter(), rhs.iter())
+                        .all(|(lhs, rhs)| self.types_may_unify(lhs, rhs))
+            }
 
-            ty::CoroutineWitness(..) => {
-                panic!("unexpected obligation type: {:?}", obligation_ty)
+            (ty::RawPtr(lhs_ty, lhs_mutbl), ty::RawPtr(rhs_ty, rhs_mutbl)) => {
+                lhs_mutbl == rhs_mutbl && self.types_may_unify(lhs_ty, rhs_ty)
             }
-        }
-    }
 
-    pub fn consts_may_unify(self, obligation_ct: I::Const, impl_ct: I::Const) -> bool {
-        let impl_val = match impl_ct.kind() {
-            ty::ConstKind::Expr(_)
-            | ty::ConstKind::Param(_)
-            | ty::ConstKind::Unevaluated(_)
-            | ty::ConstKind::Error(_) => {
-                return true;
+            (ty::Dynamic(lhs_preds, ..), ty::Dynamic(rhs_preds, ..)) => {
+                // Ideally we would walk the existential predicates here or at least
+                // compare their length. But considering that the relevant `Relate` impl
+                // actually sorts and deduplicates these, that doesn't work.
+                lhs_preds.principal_def_id() == rhs_preds.principal_def_id()
             }
-            ty::ConstKind::Value(_, impl_val) => impl_val,
-            ty::ConstKind::Infer(_) | ty::ConstKind::Bound(..) | ty::ConstKind::Placeholder(_) => {
-                panic!("unexpected impl arg: {:?}", impl_ct)
+
+            (ty::FnPtr(lhs_sig), ty::FnPtr(rhs_sig)) => {
+                let lhs_sig = lhs_sig.skip_binder();
+                let rhs_sig = rhs_sig.skip_binder();
+
+                lhs_sig.abi == rhs_sig.abi
+                    && lhs_sig.c_variadic == rhs_sig.c_variadic
+                    && lhs_sig.safety == rhs_sig.safety
+                    && lhs_sig.inputs_and_output.len() == rhs_sig.inputs_and_output.len()
+                    && iter::zip(lhs_sig.inputs_and_output.iter(), rhs_sig.inputs_and_output.iter())
+                        .all(|(lhs, rhs)| self.types_may_unify(lhs, rhs))
             }
-        };
 
-        match obligation_ct.kind() {
-            ty::ConstKind::Param(_) => match self.treat_obligation_params {
-                TreatParams::ForLookup => false,
-                TreatParams::AsCandidateKey => true,
-            },
+            (ty::FnDef(lhs_def_id, lhs_args), ty::FnDef(rhs_def_id, rhs_args))
+            | (ty::Closure(lhs_def_id, lhs_args), ty::Closure(rhs_def_id, rhs_args))
+            | (
+                ty::CoroutineClosure(lhs_def_id, lhs_args),
+                ty::CoroutineClosure(rhs_def_id, rhs_args),
+            )
+            | (ty::Coroutine(lhs_def_id, lhs_args), ty::Coroutine(rhs_def_id, rhs_args))
+            | (
+                ty::CoroutineWitness(lhs_def_id, lhs_args),
+                ty::CoroutineWitness(rhs_def_id, rhs_args),
+            ) => lhs_def_id == rhs_def_id && self.args_may_unify(lhs_args, rhs_args),
 
-            // Placeholder consts don't unify with anything on their own
-            ty::ConstKind::Placeholder(_) => false,
+            (ty::Placeholder(_), _)
+            | (_, ty::Placeholder(_))
+            | (ty::Bool, _)
+            | (_, ty::Bool)
+            | (ty::Char, _)
+            | (_, ty::Char)
+            | (ty::Int(_), _)
+            | (_, ty::Int(_))
+            | (ty::Uint(_), _)
+            | (_, ty::Uint(_))
+            | (ty::Float(_), _)
+            | (_, ty::Float(_))
+            | (ty::Str, _)
+            | (_, ty::Str)
+            | (ty::Never, _)
+            | (_, ty::Never)
+            | (ty::Foreign(_), _)
+            | (_, ty::Foreign(_))
+            | (ty::Ref(..), _)
+            | (_, ty::Ref(..))
+            | (ty::Adt(..), _)
+            | (_, ty::Adt(..))
+            | (ty::Pat(..), _)
+            | (_, ty::Pat(..))
+            | (ty::Slice(_), _)
+            | (_, ty::Slice(_))
+            | (ty::Array(..), _)
+            | (_, ty::Array(..))
+            | (ty::Tuple(_), _)
+            | (_, ty::Tuple(_))
+            | (ty::RawPtr(..), _)
+            | (_, ty::RawPtr(..))
+            | (ty::Dynamic(..), _)
+            | (_, ty::Dynamic(..))
+            | (ty::FnPtr(..), _)
+            | (_, ty::FnPtr(..))
+            | (ty::FnDef(..), _)
+            | (_, ty::FnDef(..))
+            | (ty::Closure(..), _)
+            | (_, ty::Closure(..))
+            | (ty::CoroutineClosure(..), _)
+            | (_, ty::CoroutineClosure(..))
+            | (ty::Coroutine(..), _)
+            | (_, ty::Coroutine(..)) => false,
+        }
+    }
 
-            // As we don't necessarily eagerly evaluate constants,
-            // they might unify with any value.
-            ty::ConstKind::Expr(_) | ty::ConstKind::Unevaluated(_) | ty::ConstKind::Error(_) => {
-                true
+    pub fn consts_may_unify(self, lhs: I::Const, rhs: I::Const) -> bool {
+        // As we don't necessarily eagerly evaluate constants, values
+        // may unify with everything except placeholder consts.
+        match (lhs.kind(), rhs.kind()) {
+            (ty::ConstKind::Value(_, lhs_val), ty::ConstKind::Value(_, rhs_val)) => {
+                lhs_val == rhs_val
             }
-            ty::ConstKind::Value(_, obl_val) => obl_val == impl_val,
 
-            ty::ConstKind::Infer(_) => true,
+            (ty::ConstKind::Value(..), ty::ConstKind::Placeholder(_))
+            | (ty::ConstKind::Placeholder(_), ty::ConstKind::Value(..)) => false,
 
-            ty::ConstKind::Bound(..) => {
-                panic!("unexpected obl const: {:?}", obligation_ct)
+            (ty::ConstKind::Param(_), ty::ConstKind::Value(..)) => {
+                self.treat_lhs_params == TreatParams::InstantiateWithInfer
+            }
+            (ty::ConstKind::Value(..), ty::ConstKind::Param(_)) => {
+                self.treat_rhs_params == TreatParams::InstantiateWithInfer
             }
+
+            _ => true,
+        }
+    }
+
+    fn var_and_ty_may_unify(self, var: ty::InferTy, ty: I::Ty) -> bool {
+        if !ty.is_known_rigid() {
+            return true;
+        }
+
+        match var {
+            ty::IntVar(_) => ty.is_integral(),
+            ty::FloatVar(_) => ty.is_floating_point(),
+            _ => true,
         }
     }
 }
diff --git a/src/librustdoc/html/render/write_shared.rs b/src/librustdoc/html/render/write_shared.rs
index 8fd56eae37ffc..589b7ef96ae70 100644
--- a/src/librustdoc/html/render/write_shared.rs
+++ b/src/librustdoc/html/render/write_shared.rs
@@ -507,7 +507,11 @@ else if (window.initSearch) window.initSearch(searchIndex);
                 // Be aware of `tests/rustdoc/type-alias/deeply-nested-112515.rs` which might regress.
                 let Some(impl_did) = impl_item_id.as_def_id() else { continue };
                 let for_ty = self.cx.tcx().type_of(impl_did).skip_binder();
-                let reject_cx = DeepRejectCtxt::new(self.cx.tcx(), TreatParams::AsCandidateKey);
+                let reject_cx = DeepRejectCtxt::new(
+                    self.cx.tcx(),
+                    TreatParams::InstantiateWithInfer,
+                    TreatParams::InstantiateWithInfer,
+                );
                 if !reject_cx.types_may_unify(aliased_ty, for_ty) {
                     continue;
                 }