diff --git a/library/core/src/bstr/traits.rs b/library/core/src/bstr/traits.rs
index 1d8d0e29e9a5a..6e9d836f1a1ff 100644
--- a/library/core/src/bstr/traits.rs
+++ b/library/core/src/bstr/traits.rs
@@ -6,7 +6,8 @@ use crate::slice::SliceIndex;
 use crate::{hash, ops, range};
 
 #[unstable(feature = "bstr", issue = "134915")]
-impl Ord for ByteStr {
+#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
+const impl Ord for ByteStr {
     #[inline]
     fn cmp(&self, other: &ByteStr) -> Ordering {
         Ord::cmp(&self.0, &other.0)
@@ -14,7 +15,8 @@ impl Ord for ByteStr {
 }
 
 #[unstable(feature = "bstr", issue = "134915")]
-impl PartialOrd for ByteStr {
+#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
+const impl PartialOrd for ByteStr {
     #[inline]
     fn partial_cmp(&self, other: &ByteStr) -> Option<Ordering> {
         PartialOrd::partial_cmp(&self.0, &other.0)
@@ -22,7 +24,8 @@ impl PartialOrd for ByteStr {
 }
 
 #[unstable(feature = "bstr", issue = "134915")]
-impl PartialEq<ByteStr> for ByteStr {
+#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
+const impl PartialEq<ByteStr> for ByteStr {
     #[inline]
     fn eq(&self, other: &ByteStr) -> bool {
         self.0 == other.0
@@ -30,7 +33,8 @@ impl PartialEq<ByteStr> for ByteStr {
 }
 
 #[unstable(feature = "bstr", issue = "134915")]
-impl Eq for ByteStr {}
+#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
+const impl Eq for ByteStr {}
 
 #[unstable(feature = "bstr", issue = "134915")]
 impl hash::Hash for ByteStr {
diff --git a/library/core/src/ffi/c_str.rs b/library/core/src/ffi/c_str.rs
index e5b1f8088a5bf..e575c269bd936 100644
--- a/library/core/src/ffi/c_str.rs
+++ b/library/core/src/ffi/c_str.rs
@@ -88,7 +88,8 @@ use crate::{fmt, ops, range, slice, str};
 /// ```
 ///
 /// [str]: prim@str "str"
-#[derive(PartialEq, Eq, Hash)]
+#[derive(Hash)]
+#[derive_const(PartialEq, Eq)]
 #[stable(feature = "core_c_str", since = "1.64.0")]
 #[rustc_diagnostic_item = "cstr_type"]
 #[rustc_has_incoherent_inherent_impls]
@@ -684,7 +685,8 @@ impl PartialEq<&Self> for CStr {
 // because `c_char` is `i8` (not `u8`) on some platforms.
 // That is why this is implemented manually and not derived.
 #[stable(feature = "rust1", since = "1.0.0")]
-impl PartialOrd for CStr {
+#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
+const impl PartialOrd for CStr {
     #[inline]
     fn partial_cmp(&self, other: &CStr) -> Option<Ordering> {
         self.to_bytes().partial_cmp(other.to_bytes())
@@ -692,7 +694,8 @@ impl PartialOrd for CStr {
 }
 
 #[stable(feature = "rust1", since = "1.0.0")]
-impl Ord for CStr {
+#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
+const impl Ord for CStr {
     #[inline]
     fn cmp(&self, other: &CStr) -> Ordering {
         self.to_bytes().cmp(other.to_bytes())
diff --git a/library/core/src/panic/location.rs b/library/core/src/panic/location.rs
index f37f5370997e1..4fa911272e136 100644
--- a/library/core/src/panic/location.rs
+++ b/library/core/src/panic/location.rs
@@ -47,7 +47,8 @@ pub struct Location<'a> {
 }
 
 #[stable(feature = "panic_hooks", since = "1.10.0")]
-impl PartialEq for Location<'_> {
+#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
+const impl PartialEq for Location<'_> {
     fn eq(&self, other: &Self) -> bool {
         // Compare col / line first as they're cheaper to compare and more likely to differ,
         // while not impacting the result.
@@ -56,20 +57,23 @@ impl PartialEq for Location<'_> {
 }
 
 #[stable(feature = "panic_hooks", since = "1.10.0")]
-impl Eq for Location<'_> {}
+#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
+const impl Eq for Location<'_> {}
 
 #[stable(feature = "panic_hooks", since = "1.10.0")]
-impl Ord for Location<'_> {
+#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
+const impl Ord for Location<'_> {
     fn cmp(&self, other: &Self) -> Ordering {
         self.file()
             .cmp(other.file())
-            .then_with(|| self.line.cmp(&other.line))
-            .then_with(|| self.col.cmp(&other.col))
+            .then_with(const || self.line.cmp(&other.line))
+            .then_with(const || self.col.cmp(&other.col))
     }
 }
 
 #[stable(feature = "panic_hooks", since = "1.10.0")]
-impl PartialOrd for Location<'_> {
+#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
+const impl PartialOrd for Location<'_> {
     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
         Some(self.cmp(other))
     }
diff --git a/library/core/src/str/traits.rs b/library/core/src/str/traits.rs
index e4bf752ad2ae6..a72237fd0e8f8 100644
--- a/library/core/src/str/traits.rs
+++ b/library/core/src/str/traits.rs
@@ -15,7 +15,8 @@ use crate::{ops, range};
 /// culturally-accepted standards requires locale-specific data that is outside the scope of
 /// the `str` type.
 #[stable(feature = "rust1", since = "1.0.0")]
-impl Ord for str {
+#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
+const impl Ord for str {
     #[inline]
     fn cmp(&self, other: &str) -> Ordering {
         self.as_bytes().cmp(other.as_bytes())
@@ -43,7 +44,8 @@ const impl Eq for str {}
 /// culturally-accepted standards requires locale-specific data that is outside the scope of
 /// the `str` type.
 #[stable(feature = "rust1", since = "1.0.0")]
-impl PartialOrd for str {
+#[rustc_const_unstable(feature = "const_cmp", issue = "143800")]
+const impl PartialOrd for str {
     #[inline]
     fn partial_cmp(&self, other: &str) -> Option<Ordering> {
         Some(self.cmp(other))