diff --git a/library/core/src/hash/sip.rs b/library/core/src/hash/sip.rs
index 17f2caaa0c083..6ea3241c59354 100644
--- a/library/core/src/hash/sip.rs
+++ b/library/core/src/hash/sip.rs
@@ -147,9 +147,8 @@ impl SipHasher {
     #[inline]
     #[stable(feature = "rust1", since = "1.0.0")]
     #[deprecated(since = "1.13.0", note = "use `std::hash::DefaultHasher` instead")]
-    #[rustc_const_unstable(feature = "const_hash", issue = "104061")]
     #[must_use]
-    pub const fn new() -> SipHasher {
+    pub fn new() -> SipHasher {
         SipHasher::new_with_keys(0, 0)
     }
 
@@ -157,9 +156,8 @@ impl SipHasher {
     #[inline]
     #[stable(feature = "rust1", since = "1.0.0")]
     #[deprecated(since = "1.13.0", note = "use `std::hash::DefaultHasher` instead")]
-    #[rustc_const_unstable(feature = "const_hash", issue = "104061")]
     #[must_use]
-    pub const fn new_with_keys(key0: u64, key1: u64) -> SipHasher {
+    pub fn new_with_keys(key0: u64, key1: u64) -> SipHasher {
         SipHasher(SipHasher24 { hasher: Hasher::new_with_keys(key0, key1) })
     }
 }
@@ -169,8 +167,7 @@ impl SipHasher13 {
     #[inline]
     #[unstable(feature = "hashmap_internals", issue = "none")]
     #[deprecated(since = "1.13.0", note = "use `std::hash::DefaultHasher` instead")]
-    #[rustc_const_unstable(feature = "const_hash", issue = "104061")]
-    pub const fn new() -> SipHasher13 {
+    pub fn new() -> SipHasher13 {
         SipHasher13::new_with_keys(0, 0)
     }
 
@@ -178,8 +175,7 @@ impl SipHasher13 {
     #[inline]
     #[unstable(feature = "hashmap_internals", issue = "none")]
     #[deprecated(since = "1.13.0", note = "use `std::hash::DefaultHasher` instead")]
-    #[rustc_const_unstable(feature = "const_hash", issue = "104061")]
-    pub const fn new_with_keys(key0: u64, key1: u64) -> SipHasher13 {
+    pub fn new_with_keys(key0: u64, key1: u64) -> SipHasher13 {
         SipHasher13 { hasher: Hasher::new_with_keys(key0, key1) }
     }
 }
diff --git a/library/core/src/lib.rs b/library/core/src/lib.rs
index bbfe32027e8eb..87e8f28081e79 100644
--- a/library/core/src/lib.rs
+++ b/library/core/src/lib.rs
@@ -120,7 +120,6 @@
 #![feature(const_eval_select)]
 #![feature(const_exact_div)]
 #![feature(const_float_methods)]
-#![feature(const_hash)]
 #![feature(const_heap)]
 #![feature(const_nonnull_new)]
 #![feature(const_option_ext)]
diff --git a/library/core/tests/lib.rs b/library/core/tests/lib.rs
index 7346d9f231939..db64dba21251a 100644
--- a/library/core/tests/lib.rs
+++ b/library/core/tests/lib.rs
@@ -19,7 +19,6 @@
 #![feature(const_align_offset)]
 #![feature(const_black_box)]
 #![feature(const_eval_select)]
-#![feature(const_hash)]
 #![feature(const_heap)]
 #![feature(const_nonnull_new)]
 #![feature(const_option_ext)]
diff --git a/library/std/src/collections/hash/map/tests.rs b/library/std/src/collections/hash/map/tests.rs
index b79ad1c3119ff..a275488a55602 100644
--- a/library/std/src/collections/hash/map/tests.rs
+++ b/library/std/src/collections/hash/map/tests.rs
@@ -5,7 +5,7 @@ use super::Entry::{Occupied, Vacant};
 use super::HashMap;
 use crate::assert_matches::assert_matches;
 use crate::cell::RefCell;
-use crate::hash::RandomState;
+use crate::hash::{BuildHasher, BuildHasherDefault, DefaultHasher, RandomState};
 use crate::test_helpers::test_rng;
 
 // https://github.com/rust-lang/rust/issues/62301
@@ -1124,6 +1124,26 @@ fn from_array() {
 
 #[test]
 fn const_with_hasher() {
-    const X: HashMap<(), (), ()> = HashMap::with_hasher(());
-    assert_eq!(X.len(), 0);
+    const X: HashMap<(), (), BuildHasherDefault<DefaultHasher>> =
+        HashMap::with_hasher(BuildHasherDefault::new());
+    let mut x = X;
+    assert_eq!(x.len(), 0);
+    x.insert((), ());
+    assert_eq!(x.len(), 1);
+
+    // It *is* possible to do this without using the `BuildHasherDefault` type.
+    struct MyBuildDefaultHasher;
+    impl BuildHasher for MyBuildDefaultHasher {
+        type Hasher = DefaultHasher;
+
+        fn build_hasher(&self) -> Self::Hasher {
+            DefaultHasher::new()
+        }
+    }
+
+    const Y: HashMap<(), (), MyBuildDefaultHasher> = HashMap::with_hasher(MyBuildDefaultHasher);
+    let mut y = Y;
+    assert_eq!(y.len(), 0);
+    y.insert((), ());
+    assert_eq!(y.len(), 1);
 }
diff --git a/library/std/src/hash/random.rs b/library/std/src/hash/random.rs
index 40f3a90f60c8a..236803b24a2ec 100644
--- a/library/std/src/hash/random.rs
+++ b/library/std/src/hash/random.rs
@@ -105,9 +105,8 @@ impl DefaultHasher {
     #[stable(feature = "hashmap_default_hasher", since = "1.13.0")]
     #[inline]
     #[allow(deprecated)]
-    #[rustc_const_unstable(feature = "const_hash", issue = "104061")]
     #[must_use]
-    pub const fn new() -> DefaultHasher {
+    pub fn new() -> DefaultHasher {
         DefaultHasher(SipHasher13::new_with_keys(0, 0))
     }
 }
diff --git a/library/std/src/lib.rs b/library/std/src/lib.rs
index d0dd991a93395..b5450d0a20cf2 100644
--- a/library/std/src/lib.rs
+++ b/library/std/src/lib.rs
@@ -328,6 +328,7 @@
 // Library features (core):
 // tidy-alphabetical-start
 #![feature(array_chunks)]
+#![feature(build_hasher_default_const_new)]
 #![feature(c_str_module)]
 #![feature(char_internals)]
 #![feature(clone_to_uninit)]
@@ -415,7 +416,6 @@
 // Only for const-ness:
 // tidy-alphabetical-start
 #![feature(const_collections_with_hasher)]
-#![feature(const_hash)]
 #![feature(thread_local_internals)]
 // tidy-alphabetical-end
 //