diff --git a/tests/ui/traits/new-solver/param-candidate-doesnt-shadow-project.rs b/tests/ui/traits/new-solver/param-candidate-doesnt-shadow-project.rs
new file mode 100644
index 0000000000000..bdf999ec5dd00
--- /dev/null
+++ b/tests/ui/traits/new-solver/param-candidate-doesnt-shadow-project.rs
@@ -0,0 +1,25 @@
+// compile-flags: -Ztrait-solver=next
+// check-pass
+
+trait Foo {
+    type Assoc;
+}
+
+trait Bar {}
+
+impl<T> Foo for T {
+    type Assoc = i32;
+}
+
+impl<T> Bar for T where T: Foo<Assoc = i32> {}
+
+fn require_bar<T: Bar>() {}
+
+fn foo<T: Foo>() {
+    // Unlike the classic solver, `<T as Foo>::Assoc = _` will still project
+    // down to `i32` even though there's a param-env candidate here, since we
+    // don't assemble any param-env projection candidates for `T: Foo` alone.
+    require_bar::<T>();
+}
+
+fn main() {}
diff --git a/tests/ui/traits/new-solver/two-projection-param-candidates-are-ambiguous.rs b/tests/ui/traits/new-solver/two-projection-param-candidates-are-ambiguous.rs
new file mode 100644
index 0000000000000..cde2059ca9b91
--- /dev/null
+++ b/tests/ui/traits/new-solver/two-projection-param-candidates-are-ambiguous.rs
@@ -0,0 +1,30 @@
+// compile-flags: -Ztrait-solver=next
+
+// When we're solving `<T as Foo>::Assoc = i32`, we actually first solve
+// `<T as Foo>::Assoc = _#1t`, then unify `_#1t` with `i32`. That goal
+// with the inference variable is ambiguous when there are >1 param-env
+// candidates.
+
+// We don't unify the RHS of a projection goal eagerly when solving, both
+// for caching reasons and partly to make sure that we don't make the new
+// trait solver smarter than it should be.
+
+// This is (as far as I can tell) a forwards-compatible decision, but if you
+// make this test go from fail to pass, be sure you understand the implications!
+
+trait Foo {
+    type Assoc;
+}
+
+trait Bar {}
+
+impl<T> Bar for T where T: Foo<Assoc = i32> {}
+
+fn needs_bar<T: Bar>() {}
+
+fn foo<T: Foo<Assoc = i32> + Foo<Assoc = u32>>() {
+    needs_bar::<T>();
+    //~^ ERROR type annotations needed: cannot satisfy `T: Bar`
+}
+
+fn main() {}
diff --git a/tests/ui/traits/new-solver/two-projection-param-candidates-are-ambiguous.stderr b/tests/ui/traits/new-solver/two-projection-param-candidates-are-ambiguous.stderr
new file mode 100644
index 0000000000000..fa5e780ee5e8b
--- /dev/null
+++ b/tests/ui/traits/new-solver/two-projection-param-candidates-are-ambiguous.stderr
@@ -0,0 +1,16 @@
+error[E0283]: type annotations needed: cannot satisfy `T: Bar`
+  --> $DIR/two-projection-param-candidates-are-ambiguous.rs:26:5
+   |
+LL |     needs_bar::<T>();
+   |     ^^^^^^^^^^^^^^
+   |
+   = note: cannot satisfy `T: Bar`
+note: required by a bound in `needs_bar`
+  --> $DIR/two-projection-param-candidates-are-ambiguous.rs:23:17
+   |
+LL | fn needs_bar<T: Bar>() {}
+   |                 ^^^ required by this bound in `needs_bar`
+
+error: aborting due to previous error
+
+For more information about this error, try `rustc --explain E0283`.