diff --git a/compiler/rustc_abi/src/lib.rs b/compiler/rustc_abi/src/lib.rs
index 85693259cd0..e14c9ea9a5d 100644
--- a/compiler/rustc_abi/src/lib.rs
+++ b/compiler/rustc_abi/src/lib.rs
@@ -9,6 +9,8 @@ use std::ops::{Add, AddAssign, Mul, RangeInclusive, Sub};
 use std::str::FromStr;
 
 use bitflags::bitflags;
+#[cfg(feature = "nightly")]
+use rustc_data_structures::stable_hasher::StableOrd;
 use rustc_index::vec::{Idx, IndexVec};
 #[cfg(feature = "nightly")]
 use rustc_macros::HashStable_Generic;
@@ -403,6 +405,11 @@ pub struct Size {
     raw: u64,
 }
 
+// Safety: Ord is implement as just comparing numerical values and numerical values
+// are not changed by (de-)serialization.
+#[cfg(feature = "nightly")]
+unsafe impl StableOrd for Size {}
+
 // This is debug-printed a lot in larger structs, don't waste too much space there
 impl fmt::Debug for Size {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
diff --git a/compiler/rustc_data_structures/src/fingerprint.rs b/compiler/rustc_data_structures/src/fingerprint.rs
index a39178016ce..6f0b9bff90a 100644
--- a/compiler/rustc_data_structures/src/fingerprint.rs
+++ b/compiler/rustc_data_structures/src/fingerprint.rs
@@ -140,7 +140,7 @@ impl stable_hasher::StableHasherResult for Fingerprint {
     }
 }
 
-impl_stable_hash_via_hash!(Fingerprint);
+impl_stable_ord_and_stable_hash_via_hash!(Fingerprint);
 
 impl<E: Encoder> Encodable<E> for Fingerprint {
     #[inline]
diff --git a/compiler/rustc_data_structures/src/sorted_map.rs b/compiler/rustc_data_structures/src/sorted_map.rs
index d607a5c8314..d13313dfd0e 100644
--- a/compiler/rustc_data_structures/src/sorted_map.rs
+++ b/compiler/rustc_data_structures/src/sorted_map.rs
@@ -1,4 +1,4 @@
-use crate::stable_hasher::{HashStable, StableHasher};
+use crate::stable_hasher::{HashStable, StableHasher, StableOrd};
 use std::borrow::Borrow;
 use std::cmp::Ordering;
 use std::iter::FromIterator;
@@ -308,7 +308,7 @@ impl<K: Ord, V> FromIterator<(K, V)> for SortedMap<K, V> {
     }
 }
 
-impl<K: HashStable<CTX>, V: HashStable<CTX>, CTX> HashStable<CTX> for SortedMap<K, V> {
+impl<K: HashStable<CTX> + StableOrd, V: HashStable<CTX>, CTX> HashStable<CTX> for SortedMap<K, V> {
     #[inline]
     fn hash_stable(&self, ctx: &mut CTX, hasher: &mut StableHasher) {
         self.data.hash_stable(ctx, hasher);
diff --git a/compiler/rustc_data_structures/src/sorted_map/index_map.rs b/compiler/rustc_data_structures/src/sorted_map/index_map.rs
index 0ec32dc4307..c2f0ae32896 100644
--- a/compiler/rustc_data_structures/src/sorted_map/index_map.rs
+++ b/compiler/rustc_data_structures/src/sorted_map/index_map.rs
@@ -120,13 +120,20 @@ where
         self.items.hash(hasher)
     }
 }
+
 impl<I: Idx, K, V, C> HashStable<C> for SortedIndexMultiMap<I, K, V>
 where
     K: HashStable<C>,
     V: HashStable<C>,
 {
     fn hash_stable(&self, ctx: &mut C, hasher: &mut StableHasher) {
-        self.items.hash_stable(ctx, hasher)
+        let SortedIndexMultiMap {
+            items,
+            // We can ignore this field because it is not observable from the outside.
+            idx_sorted_by_item_key: _,
+        } = self;
+
+        items.hash_stable(ctx, hasher)
     }
 }
 
diff --git a/compiler/rustc_data_structures/src/stable_hasher.rs b/compiler/rustc_data_structures/src/stable_hasher.rs
index e2c33e7e062..d43b74c2740 100644
--- a/compiler/rustc_data_structures/src/stable_hasher.rs
+++ b/compiler/rustc_data_structures/src/stable_hasher.rs
@@ -219,7 +219,35 @@ pub trait ToStableHashKey<HCX> {
     fn to_stable_hash_key(&self, hcx: &HCX) -> Self::KeyType;
 }
 
-/// Implement HashStable by just calling `Hash::hash()`.
+/// Trait for marking a type as having a sort order that is
+/// stable across compilation session boundaries. More formally:
+///
+/// ```txt
+/// Ord::cmp(a1, b1) == Ord:cmp(a2, b2)
+///    where a2 = decode(encode(a1, context1), context2)
+///          b2 = decode(encode(b1, context1), context2)
+/// ```
+///
+/// i.e. the result of `Ord::cmp` is not influenced by encoding
+/// the values in one session and then decoding them in another
+/// session.
+///
+/// This is trivially true for types where encoding and decoding
+/// don't change the bytes of the values that are used during
+/// comparison and comparison only depends on these bytes (as
+/// opposed to some non-local state). Examples are u32, String,
+/// Path, etc.
+///
+/// But it is not true for:
+///  - `*const T` and `*mut T` because the values of these pointers
+///    will change between sessions.
+///  - `DefIndex`, `CrateNum`, `LocalDefId`, because their concrete
+///    values depend on state that might be different between
+///    compilation sessions.
+pub unsafe trait StableOrd: Ord {}
+
+/// Implement HashStable by just calling `Hash::hash()`. Also implement `StableOrd` for the type since
+/// that has the same requirements.
 ///
 /// **WARNING** This is only valid for types that *really* don't need any context for fingerprinting.
 /// But it is easy to misuse this macro (see [#96013](https://github.com/rust-lang/rust/issues/96013)
@@ -227,7 +255,7 @@ pub trait ToStableHashKey<HCX> {
 /// here in this module.
 ///
 /// Use `#[derive(HashStable_Generic)]` instead.
-macro_rules! impl_stable_hash_via_hash {
+macro_rules! impl_stable_ord_and_stable_hash_via_hash {
     ($t:ty) => {
         impl<CTX> $crate::stable_hasher::HashStable<CTX> for $t {
             #[inline]
@@ -235,26 +263,28 @@ macro_rules! impl_stable_hash_via_hash {
                 ::std::hash::Hash::hash(self, hasher);
             }
         }
+
+        unsafe impl $crate::stable_hasher::StableOrd for $t {}
     };
 }
 
-impl_stable_hash_via_hash!(i8);
-impl_stable_hash_via_hash!(i16);
-impl_stable_hash_via_hash!(i32);
-impl_stable_hash_via_hash!(i64);
-impl_stable_hash_via_hash!(isize);
+impl_stable_ord_and_stable_hash_via_hash!(i8);
+impl_stable_ord_and_stable_hash_via_hash!(i16);
+impl_stable_ord_and_stable_hash_via_hash!(i32);
+impl_stable_ord_and_stable_hash_via_hash!(i64);
+impl_stable_ord_and_stable_hash_via_hash!(isize);
 
-impl_stable_hash_via_hash!(u8);
-impl_stable_hash_via_hash!(u16);
-impl_stable_hash_via_hash!(u32);
-impl_stable_hash_via_hash!(u64);
-impl_stable_hash_via_hash!(usize);
+impl_stable_ord_and_stable_hash_via_hash!(u8);
+impl_stable_ord_and_stable_hash_via_hash!(u16);
+impl_stable_ord_and_stable_hash_via_hash!(u32);
+impl_stable_ord_and_stable_hash_via_hash!(u64);
+impl_stable_ord_and_stable_hash_via_hash!(usize);
 
-impl_stable_hash_via_hash!(u128);
-impl_stable_hash_via_hash!(i128);
+impl_stable_ord_and_stable_hash_via_hash!(u128);
+impl_stable_ord_and_stable_hash_via_hash!(i128);
 
-impl_stable_hash_via_hash!(char);
-impl_stable_hash_via_hash!(());
+impl_stable_ord_and_stable_hash_via_hash!(char);
+impl_stable_ord_and_stable_hash_via_hash!(());
 
 impl<CTX> HashStable<CTX> for ! {
     fn hash_stable(&self, _ctx: &mut CTX, _hasher: &mut StableHasher) {
@@ -444,6 +474,10 @@ impl<CTX> HashStable<CTX> for String {
     }
 }
 
+// Safety: String comparison only depends on their contents and the
+// contents are not changed by (de-)serialization.
+unsafe impl StableOrd for String {}
+
 impl<HCX> ToStableHashKey<HCX> for String {
     type KeyType = String;
     #[inline]
@@ -459,6 +493,9 @@ impl<CTX> HashStable<CTX> for bool {
     }
 }
 
+// Safety: sort order of bools is not changed by (de-)serialization.
+unsafe impl StableOrd for bool {}
+
 impl<T, CTX> HashStable<CTX> for Option<T>
 where
     T: HashStable<CTX>,
@@ -474,6 +511,9 @@ where
     }
 }
 
+// Safety: the Option wrapper does not add instability to comparison.
+unsafe impl<T: StableOrd> StableOrd for Option<T> {}
+
 impl<T1, T2, CTX> HashStable<CTX> for Result<T1, T2>
 where
     T1: HashStable<CTX>,
@@ -550,8 +590,8 @@ where
     }
 }
 
-impl_stable_hash_via_hash!(::std::path::Path);
-impl_stable_hash_via_hash!(::std::path::PathBuf);
+impl_stable_ord_and_stable_hash_via_hash!(::std::path::Path);
+impl_stable_ord_and_stable_hash_via_hash!(::std::path::PathBuf);
 
 impl<K, V, R, HCX> HashStable<HCX> for ::std::collections::HashMap<K, V, R>
 where
@@ -584,27 +624,26 @@ where
 
 impl<K, V, HCX> HashStable<HCX> for ::std::collections::BTreeMap<K, V>
 where
-    K: ToStableHashKey<HCX>,
+    K: HashStable<HCX> + StableOrd,
     V: HashStable<HCX>,
 {
     fn hash_stable(&self, hcx: &mut HCX, hasher: &mut StableHasher) {
-        stable_hash_reduce(hcx, hasher, self.iter(), self.len(), |hasher, hcx, (key, value)| {
-            let key = key.to_stable_hash_key(hcx);
-            key.hash_stable(hcx, hasher);
-            value.hash_stable(hcx, hasher);
-        });
+        self.len().hash_stable(hcx, hasher);
+        for entry in self.iter() {
+            entry.hash_stable(hcx, hasher);
+        }
     }
 }
 
-impl<K, HCX> HashStable<HCX> for ::std::collections::BTreeSet<K>
+impl<K: StableOrd, HCX> HashStable<HCX> for ::std::collections::BTreeSet<K>
 where
-    K: ToStableHashKey<HCX>,
+    K: HashStable<HCX> + StableOrd,
 {
     fn hash_stable(&self, hcx: &mut HCX, hasher: &mut StableHasher) {
-        stable_hash_reduce(hcx, hasher, self.iter(), self.len(), |hasher, hcx, key| {
-            let key = key.to_stable_hash_key(hcx);
-            key.hash_stable(hcx, hasher);
-        });
+        self.len().hash_stable(hcx, hasher);
+        for entry in self.iter() {
+            entry.hash_stable(hcx, hasher);
+        }
     }
 }
 
diff --git a/compiler/rustc_hir/src/hir_id.rs b/compiler/rustc_hir/src/hir_id.rs
index 33f02a115ef..9f7e79596e9 100644
--- a/compiler/rustc_hir/src/hir_id.rs
+++ b/compiler/rustc_hir/src/hir_id.rs
@@ -1,5 +1,5 @@
 use crate::def_id::{DefId, DefIndex, LocalDefId, CRATE_DEF_ID};
-use rustc_data_structures::stable_hasher::{HashStable, StableHasher, ToStableHashKey};
+use rustc_data_structures::stable_hasher::{HashStable, StableHasher, StableOrd, ToStableHashKey};
 use rustc_span::{def_id::DefPathHash, HashStableContext};
 use std::fmt;
 
@@ -146,6 +146,10 @@ impl ItemLocalId {
     pub const INVALID: ItemLocalId = ItemLocalId::MAX;
 }
 
+// Safety: Ord is implement as just comparing the LocalItemId's numerical
+// values and these are not changed by (de-)serialization.
+unsafe impl StableOrd for ItemLocalId {}
+
 /// The `HirId` corresponding to `CRATE_NODE_ID` and `CRATE_DEF_ID`.
 pub const CRATE_HIR_ID: HirId =
     HirId { owner: OwnerId { def_id: CRATE_DEF_ID }, local_id: ItemLocalId::from_u32(0) };
diff --git a/compiler/rustc_session/src/config.rs b/compiler/rustc_session/src/config.rs
index 927810351e9..5dcd53e8e51 100644
--- a/compiler/rustc_session/src/config.rs
+++ b/compiler/rustc_session/src/config.rs
@@ -10,7 +10,7 @@ use crate::{lint, HashStableContext};
 
 use rustc_data_structures::fx::{FxHashMap, FxHashSet};
 
-use rustc_data_structures::stable_hasher::ToStableHashKey;
+use rustc_data_structures::stable_hasher::{StableOrd, ToStableHashKey};
 use rustc_target::abi::Align;
 use rustc_target::spec::{PanicStrategy, SanitizerSet, SplitDebuginfo};
 use rustc_target::spec::{Target, TargetTriple, TargetWarnings, TARGETS};
@@ -288,6 +288,9 @@ pub enum OutputType {
     DepInfo,
 }
 
+// Safety: Trivial C-Style enums have a stable sort order across compilation sessions.
+unsafe impl StableOrd for OutputType {}
+
 impl<HCX: HashStableContext> ToStableHashKey<HCX> for OutputType {
     type KeyType = Self;