diff --git a/compiler/rustc_data_structures/src/lib.rs b/compiler/rustc_data_structures/src/lib.rs
index 467ac401d086b..3a2000233c5d1 100644
--- a/compiler/rustc_data_structures/src/lib.rs
+++ b/compiler/rustc_data_structures/src/lib.rs
@@ -22,6 +22,7 @@
 #![feature(new_uninit)]
 #![feature(once_cell)]
 #![feature(rustc_attrs)]
+#![feature(negative_impls)]
 #![feature(test)]
 #![feature(thread_id_value)]
 #![feature(vec_into_raw_parts)]
@@ -86,6 +87,7 @@ pub mod steal;
 pub mod tagged_ptr;
 pub mod temp_dir;
 pub mod unhash;
+pub mod unord;
 
 pub use ena::undo_log;
 pub use ena::unify;
diff --git a/compiler/rustc_data_structures/src/unord.rs b/compiler/rustc_data_structures/src/unord.rs
new file mode 100644
index 0000000000000..c015f1232cd92
--- /dev/null
+++ b/compiler/rustc_data_structures/src/unord.rs
@@ -0,0 +1,382 @@
+//! This module contains collection types that don't expose their internal
+//! ordering. This is a useful property for deterministic computations, such
+//! as required by the query system.
+
+use rustc_hash::{FxHashMap, FxHashSet};
+use smallvec::SmallVec;
+use std::{
+    borrow::Borrow,
+    hash::Hash,
+    iter::{Product, Sum},
+};
+
+use crate::{
+    fingerprint::Fingerprint,
+    stable_hasher::{HashStable, StableHasher, ToStableHashKey},
+};
+
+/// `UnordItems` is the order-less version of `Iterator`. It only contains methods
+/// that don't (easily) expose an ordering of the underlying items.
+///
+/// Most methods take an `Fn` where the `Iterator`-version takes an `FnMut`. This
+/// is to reduce the risk of accidentally leaking the internal order via the closure
+/// environment. Otherwise one could easily do something like
+///
+/// ```rust,ignore (pseudo code)
+/// let mut ordered = vec![];
+/// unordered_items.all(|x| ordered.push(x));
+/// ```
+///
+/// It's still possible to do the same thing with an `Fn` by using interior mutability,
+/// but the chance of doing it accidentally is reduced.
+pub struct UnordItems<T, I: Iterator<Item = T>>(I);
+
+impl<T, I: Iterator<Item = T>> UnordItems<T, I> {
+    #[inline]
+    pub fn map<U, F: Fn(T) -> U>(self, f: F) -> UnordItems<U, impl Iterator<Item = U>> {
+        UnordItems(self.0.map(f))
+    }
+
+    #[inline]
+    pub fn all<U, F: Fn(T) -> bool>(mut self, f: F) -> bool {
+        self.0.all(f)
+    }
+
+    #[inline]
+    pub fn any<U, F: Fn(T) -> bool>(mut self, f: F) -> bool {
+        self.0.any(f)
+    }
+
+    #[inline]
+    pub fn filter<U, F: Fn(&T) -> bool>(self, f: F) -> UnordItems<T, impl Iterator<Item = T>> {
+        UnordItems(self.0.filter(f))
+    }
+
+    #[inline]
+    pub fn filter_map<U, F: Fn(T) -> Option<U>>(
+        self,
+        f: F,
+    ) -> UnordItems<U, impl Iterator<Item = U>> {
+        UnordItems(self.0.filter_map(f))
+    }
+
+    #[inline]
+    pub fn max(self) -> Option<T>
+    where
+        T: Ord,
+    {
+        self.0.max()
+    }
+
+    #[inline]
+    pub fn min(self) -> Option<T>
+    where
+        T: Ord,
+    {
+        self.0.min()
+    }
+
+    #[inline]
+    pub fn sum<S>(self) -> S
+    where
+        S: Sum<T>,
+    {
+        self.0.sum()
+    }
+
+    #[inline]
+    pub fn product<S>(self) -> S
+    where
+        S: Product<T>,
+    {
+        self.0.product()
+    }
+
+    #[inline]
+    pub fn count(self) -> usize {
+        self.0.count()
+    }
+}
+
+impl<'a, T: Clone + 'a, I: Iterator<Item = &'a T>> UnordItems<&'a T, I> {
+    #[inline]
+    pub fn cloned(self) -> UnordItems<T, impl Iterator<Item = T>> {
+        UnordItems(self.0.cloned())
+    }
+}
+
+impl<'a, T: Copy + 'a, I: Iterator<Item = &'a T>> UnordItems<&'a T, I> {
+    #[inline]
+    pub fn copied(self) -> UnordItems<T, impl Iterator<Item = T>> {
+        UnordItems(self.0.copied())
+    }
+}
+
+impl<T: Ord, I: Iterator<Item = T>> UnordItems<T, I> {
+    pub fn into_sorted<HCX>(self, hcx: &HCX) -> Vec<T>
+    where
+        T: ToStableHashKey<HCX>,
+    {
+        let mut items: Vec<T> = self.0.collect();
+        items.sort_by_cached_key(|x| x.to_stable_hash_key(hcx));
+        items
+    }
+
+    pub fn into_sorted_small_vec<HCX, const LEN: usize>(self, hcx: &HCX) -> SmallVec<[T; LEN]>
+    where
+        T: ToStableHashKey<HCX>,
+    {
+        let mut items: SmallVec<[T; LEN]> = self.0.collect();
+        items.sort_by_cached_key(|x| x.to_stable_hash_key(hcx));
+        items
+    }
+}
+
+/// This is a set collection type that tries very hard to not expose
+/// any internal iteration. This is a useful property when trying to
+/// uphold the determinism invariants imposed by the query system.
+///
+/// This collection type is a good choice for set-like collections the
+/// keys of which don't have a semantic ordering.
+///
+/// See [MCP 533](https://github.com/rust-lang/compiler-team/issues/533)
+/// for more information.
+#[derive(Debug, Eq, PartialEq, Clone, Encodable, Decodable)]
+pub struct UnordSet<V: Eq + Hash> {
+    inner: FxHashSet<V>,
+}
+
+impl<V: Eq + Hash> Default for UnordSet<V> {
+    fn default() -> Self {
+        Self { inner: FxHashSet::default() }
+    }
+}
+
+impl<V: Eq + Hash> UnordSet<V> {
+    #[inline]
+    pub fn new() -> Self {
+        Self { inner: Default::default() }
+    }
+
+    #[inline]
+    pub fn len(&self) -> usize {
+        self.inner.len()
+    }
+
+    #[inline]
+    pub fn insert(&mut self, v: V) -> bool {
+        self.inner.insert(v)
+    }
+
+    #[inline]
+    pub fn contains<Q: ?Sized>(&self, v: &Q) -> bool
+    where
+        V: Borrow<Q>,
+        Q: Hash + Eq,
+    {
+        self.inner.contains(v)
+    }
+
+    #[inline]
+    pub fn items<'a>(&'a self) -> UnordItems<&'a V, impl Iterator<Item = &'a V>> {
+        UnordItems(self.inner.iter())
+    }
+
+    #[inline]
+    pub fn into_items(self) -> UnordItems<V, impl Iterator<Item = V>> {
+        UnordItems(self.inner.into_iter())
+    }
+
+    // We can safely extend this UnordSet from a set of unordered values because that
+    // won't expose the internal ordering anywhere.
+    #[inline]
+    pub fn extend<I: Iterator<Item = V>>(&mut self, items: UnordItems<V, I>) {
+        self.inner.extend(items.0)
+    }
+}
+
+impl<V: Hash + Eq> Extend<V> for UnordSet<V> {
+    fn extend<T: IntoIterator<Item = V>>(&mut self, iter: T) {
+        self.inner.extend(iter)
+    }
+}
+
+impl<HCX, V: Hash + Eq + HashStable<HCX>> HashStable<HCX> for UnordSet<V> {
+    #[inline]
+    fn hash_stable(&self, hcx: &mut HCX, hasher: &mut StableHasher) {
+        hash_iter_order_independent(self.inner.iter(), hcx, hasher);
+    }
+}
+
+/// This is a map collection type that tries very hard to not expose
+/// any internal iteration. This is a useful property when trying to
+/// uphold the determinism invariants imposed by the query system.
+///
+/// This collection type is a good choice for map-like collections the
+/// keys of which don't have a semantic ordering.
+///
+/// See [MCP 533](https://github.com/rust-lang/compiler-team/issues/533)
+/// for more information.
+#[derive(Debug, Eq, PartialEq, Clone, Encodable, Decodable)]
+pub struct UnordMap<K: Eq + Hash, V> {
+    inner: FxHashMap<K, V>,
+}
+
+impl<K: Eq + Hash, V> Default for UnordMap<K, V> {
+    fn default() -> Self {
+        Self { inner: FxHashMap::default() }
+    }
+}
+
+impl<K: Hash + Eq, V> Extend<(K, V)> for UnordMap<K, V> {
+    fn extend<T: IntoIterator<Item = (K, V)>>(&mut self, iter: T) {
+        self.inner.extend(iter)
+    }
+}
+
+impl<K: Eq + Hash, V> UnordMap<K, V> {
+    #[inline]
+    pub fn len(&self) -> usize {
+        self.inner.len()
+    }
+
+    #[inline]
+    pub fn insert(&mut self, k: K, v: V) -> Option<V> {
+        self.inner.insert(k, v)
+    }
+
+    #[inline]
+    pub fn contains_key<Q: ?Sized>(&self, k: &Q) -> bool
+    where
+        K: Borrow<Q>,
+        Q: Hash + Eq,
+    {
+        self.inner.contains_key(k)
+    }
+
+    #[inline]
+    pub fn items<'a>(&'a self) -> UnordItems<(&'a K, &'a V), impl Iterator<Item = (&'a K, &'a V)>> {
+        UnordItems(self.inner.iter())
+    }
+
+    #[inline]
+    pub fn into_items(self) -> UnordItems<(K, V), impl Iterator<Item = (K, V)>> {
+        UnordItems(self.inner.into_iter())
+    }
+
+    // We can safely extend this UnordMap from a set of unordered values because that
+    // won't expose the internal ordering anywhere.
+    #[inline]
+    pub fn extend<I: Iterator<Item = (K, V)>>(&mut self, items: UnordItems<(K, V), I>) {
+        self.inner.extend(items.0)
+    }
+}
+
+impl<HCX, K: Hash + Eq + HashStable<HCX>, V: HashStable<HCX>> HashStable<HCX> for UnordMap<K, V> {
+    #[inline]
+    fn hash_stable(&self, hcx: &mut HCX, hasher: &mut StableHasher) {
+        hash_iter_order_independent(self.inner.iter(), hcx, hasher);
+    }
+}
+
+/// This is a collection type that tries very hard to not expose
+/// any internal iteration. This is a useful property when trying to
+/// uphold the determinism invariants imposed by the query system.
+///
+/// This collection type is a good choice for collections the
+/// keys of which don't have a semantic ordering and don't implement
+/// `Hash` or `Eq`.
+///
+/// See [MCP 533](https://github.com/rust-lang/compiler-team/issues/533)
+/// for more information.
+#[derive(Default, Debug, Eq, PartialEq, Clone, Encodable, Decodable)]
+pub struct UnordBag<V> {
+    inner: Vec<V>,
+}
+
+impl<V> UnordBag<V> {
+    #[inline]
+    pub fn new() -> Self {
+        Self { inner: Default::default() }
+    }
+
+    #[inline]
+    pub fn len(&self) -> usize {
+        self.inner.len()
+    }
+
+    #[inline]
+    pub fn push(&mut self, v: V) {
+        self.inner.push(v);
+    }
+
+    #[inline]
+    pub fn items<'a>(&'a self) -> UnordItems<&'a V, impl Iterator<Item = &'a V>> {
+        UnordItems(self.inner.iter())
+    }
+
+    #[inline]
+    pub fn into_items(self) -> UnordItems<V, impl Iterator<Item = V>> {
+        UnordItems(self.inner.into_iter())
+    }
+
+    // We can safely extend this UnordSet from a set of unordered values because that
+    // won't expose the internal ordering anywhere.
+    #[inline]
+    pub fn extend<I: Iterator<Item = V>>(&mut self, items: UnordItems<V, I>) {
+        self.inner.extend(items.0)
+    }
+}
+
+impl<T> Extend<T> for UnordBag<T> {
+    fn extend<I: IntoIterator<Item = T>>(&mut self, iter: I) {
+        self.inner.extend(iter)
+    }
+}
+
+impl<HCX, V: Hash + Eq + HashStable<HCX>> HashStable<HCX> for UnordBag<V> {
+    #[inline]
+    fn hash_stable(&self, hcx: &mut HCX, hasher: &mut StableHasher) {
+        hash_iter_order_independent(self.inner.iter(), hcx, hasher);
+    }
+}
+
+fn hash_iter_order_independent<
+    HCX,
+    T: HashStable<HCX>,
+    I: Iterator<Item = T> + ExactSizeIterator,
+>(
+    mut it: I,
+    hcx: &mut HCX,
+    hasher: &mut StableHasher,
+) {
+    let len = it.len();
+    len.hash_stable(hcx, hasher);
+
+    match len {
+        0 => {
+            // We're done
+        }
+        1 => {
+            // No need to instantiate a hasher
+            it.next().unwrap().hash_stable(hcx, hasher);
+        }
+        _ => {
+            let mut accumulator = Fingerprint::ZERO;
+            for item in it {
+                let mut item_hasher = StableHasher::new();
+                item.hash_stable(hcx, &mut item_hasher);
+                let item_fingerprint: Fingerprint = item_hasher.finish();
+                accumulator = accumulator.combine_commutative(item_fingerprint);
+            }
+            accumulator.hash_stable(hcx, hasher);
+        }
+    }
+}
+
+// Do not implement IntoIterator for the collections in this module.
+// They only exist to hide iteration order in the first place.
+impl<T> !IntoIterator for UnordBag<T> {}
+impl<V> !IntoIterator for UnordSet<V> {}
+impl<K, V> !IntoIterator for UnordMap<K, V> {}
+impl<T, I> !IntoIterator for UnordItems<T, I> {}
diff --git a/compiler/rustc_hir_analysis/src/check_unused.rs b/compiler/rustc_hir_analysis/src/check_unused.rs
index 922833f85806c..d3df259075274 100644
--- a/compiler/rustc_hir_analysis/src/check_unused.rs
+++ b/compiler/rustc_hir_analysis/src/check_unused.rs
@@ -1,5 +1,6 @@
 use crate::errors::{ExternCrateNotIdiomatic, UnusedExternCrate};
-use rustc_data_structures::fx::{FxHashMap, FxHashSet};
+use rustc_data_structures::fx::FxHashMap;
+use rustc_data_structures::unord::UnordSet;
 use rustc_hir as hir;
 use rustc_hir::def::DefKind;
 use rustc_hir::def_id::{DefId, LocalDefId};
@@ -8,12 +9,12 @@ use rustc_session::lint;
 use rustc_span::{Span, Symbol};
 
 pub fn check_crate(tcx: TyCtxt<'_>) {
-    let mut used_trait_imports: FxHashSet<LocalDefId> = FxHashSet::default();
+    let mut used_trait_imports: UnordSet<LocalDefId> = Default::default();
 
     for item_def_id in tcx.hir().body_owners() {
         let imports = tcx.used_trait_imports(item_def_id);
         debug!("GatherVisitor: item_def_id={:?} with imports {:#?}", item_def_id, imports);
-        used_trait_imports.extend(imports.iter());
+        used_trait_imports.extend(imports.items().copied());
     }
 
     for &id in tcx.maybe_unused_trait_imports(()) {
diff --git a/compiler/rustc_hir_typeck/src/lib.rs b/compiler/rustc_hir_typeck/src/lib.rs
index e862d577573b4..959c54866453d 100644
--- a/compiler/rustc_hir_typeck/src/lib.rs
+++ b/compiler/rustc_hir_typeck/src/lib.rs
@@ -52,7 +52,7 @@ pub use inherited::{Inherited, InheritedBuilder};
 use crate::check::check_fn;
 use crate::coercion::DynamicCoerceMany;
 use crate::gather_locals::GatherLocalsVisitor;
-use rustc_data_structures::fx::FxHashSet;
+use rustc_data_structures::unord::UnordSet;
 use rustc_errors::{struct_span_err, MultiSpan};
 use rustc_hir as hir;
 use rustc_hir::def::Res;
@@ -174,7 +174,7 @@ fn has_typeck_results(tcx: TyCtxt<'_>, def_id: DefId) -> bool {
     }
 }
 
-fn used_trait_imports(tcx: TyCtxt<'_>, def_id: LocalDefId) -> &FxHashSet<LocalDefId> {
+fn used_trait_imports(tcx: TyCtxt<'_>, def_id: LocalDefId) -> &UnordSet<LocalDefId> {
     &*tcx.typeck(def_id).used_trait_imports
 }
 
diff --git a/compiler/rustc_middle/src/arena.rs b/compiler/rustc_middle/src/arena.rs
index d2847e4bc12a7..c94879c9f2139 100644
--- a/compiler/rustc_middle/src/arena.rs
+++ b/compiler/rustc_middle/src/arena.rs
@@ -96,7 +96,7 @@ macro_rules! arena_types {
             // since we need to allocate this type on both the `rustc_hir` arena
             // (during lowering) and the `librustc_middle` arena (for decoding MIR)
             [decode] asm_template: rustc_ast::InlineAsmTemplatePiece,
-            [decode] used_trait_imports: rustc_data_structures::fx::FxHashSet<rustc_hir::def_id::LocalDefId>,
+            [decode] used_trait_imports: rustc_data_structures::unord::UnordSet<rustc_hir::def_id::LocalDefId>,
             [decode] is_late_bound_map: rustc_data_structures::fx::FxIndexSet<rustc_hir::def_id::LocalDefId>,
             [decode] impl_source: rustc_middle::traits::ImplSource<'tcx, ()>,
 
diff --git a/compiler/rustc_middle/src/query/mod.rs b/compiler/rustc_middle/src/query/mod.rs
index 67c85ef0d3b50..5ee5adc371052 100644
--- a/compiler/rustc_middle/src/query/mod.rs
+++ b/compiler/rustc_middle/src/query/mod.rs
@@ -912,7 +912,7 @@ rustc_queries! {
         cache_on_disk_if { true }
     }
 
-    query used_trait_imports(key: LocalDefId) -> &'tcx FxHashSet<LocalDefId> {
+    query used_trait_imports(key: LocalDefId) -> &'tcx UnordSet<LocalDefId> {
         desc { |tcx| "finding used_trait_imports `{}`", tcx.def_path_str(key.to_def_id()) }
         cache_on_disk_if { true }
     }
diff --git a/compiler/rustc_middle/src/ty/context.rs b/compiler/rustc_middle/src/ty/context.rs
index 94e3f3b63c813..3d7e2a0839abc 100644
--- a/compiler/rustc_middle/src/ty/context.rs
+++ b/compiler/rustc_middle/src/ty/context.rs
@@ -34,6 +34,7 @@ use rustc_data_structures::sharded::{IntoPointer, ShardedHashMap};
 use rustc_data_structures::stable_hasher::{HashStable, StableHasher};
 use rustc_data_structures::steal::Steal;
 use rustc_data_structures::sync::{self, Lock, Lrc, ReadGuard, RwLock, WorkerLocal};
+use rustc_data_structures::unord::UnordSet;
 use rustc_data_structures::vec_map::VecMap;
 use rustc_errors::{
     DecorateLint, DiagnosticBuilder, DiagnosticMessage, ErrorGuaranteed, MultiSpan,
@@ -531,7 +532,7 @@ pub struct TypeckResults<'tcx> {
     /// This is used for warning unused imports. During type
     /// checking, this `Lrc` should not be cloned: it must have a ref-count
     /// of 1 so that we can insert things into the set mutably.
-    pub used_trait_imports: Lrc<FxHashSet<LocalDefId>>,
+    pub used_trait_imports: Lrc<UnordSet<LocalDefId>>,
 
     /// If any errors occurred while type-checking this body,
     /// this field will be set to `Some(ErrorGuaranteed)`.
diff --git a/compiler/rustc_middle/src/ty/query.rs b/compiler/rustc_middle/src/ty/query.rs
index 9c97ce34f29e4..1715837203c23 100644
--- a/compiler/rustc_middle/src/ty/query.rs
+++ b/compiler/rustc_middle/src/ty/query.rs
@@ -40,6 +40,7 @@ use rustc_data_structures::fx::{FxHashMap, FxHashSet, FxIndexMap, FxIndexSet};
 use rustc_data_structures::steal::Steal;
 use rustc_data_structures::svh::Svh;
 use rustc_data_structures::sync::Lrc;
+use rustc_data_structures::unord::UnordSet;
 use rustc_errors::ErrorGuaranteed;
 use rustc_hir as hir;
 use rustc_hir::def::DefKind;
diff --git a/compiler/rustc_query_impl/src/on_disk_cache.rs b/compiler/rustc_query_impl/src/on_disk_cache.rs
index a592165011273..8b14ce210a205 100644
--- a/compiler/rustc_query_impl/src/on_disk_cache.rs
+++ b/compiler/rustc_query_impl/src/on_disk_cache.rs
@@ -1,8 +1,9 @@
 use crate::QueryCtxt;
-use rustc_data_structures::fx::{FxHashMap, FxHashSet, FxIndexSet};
+use rustc_data_structures::fx::{FxHashMap, FxIndexSet};
 use rustc_data_structures::memmap::Mmap;
 use rustc_data_structures::sync::{HashMapExt, Lock, Lrc, RwLock};
 use rustc_data_structures::unhash::UnhashMap;
+use rustc_data_structures::unord::UnordSet;
 use rustc_hir::def_id::{CrateNum, DefId, DefIndex, LocalDefId, StableCrateId, LOCAL_CRATE};
 use rustc_hir::definitions::DefPathHash;
 use rustc_index::vec::{Idx, IndexVec};
@@ -792,7 +793,7 @@ impl<'a, 'tcx> Decodable<CacheDecoder<'a, 'tcx>> for DefId {
     }
 }
 
-impl<'a, 'tcx> Decodable<CacheDecoder<'a, 'tcx>> for &'tcx FxHashSet<LocalDefId> {
+impl<'a, 'tcx> Decodable<CacheDecoder<'a, 'tcx>> for &'tcx UnordSet<LocalDefId> {
     fn decode(d: &mut CacheDecoder<'a, 'tcx>) -> Self {
         RefDecodable::decode(d)
     }
diff --git a/src/librustdoc/core.rs b/src/librustdoc/core.rs
index 8232353f915b9..642acb1fea9c8 100644
--- a/src/librustdoc/core.rs
+++ b/src/librustdoc/core.rs
@@ -1,6 +1,7 @@
 use rustc_ast::NodeId;
 use rustc_data_structures::fx::{FxHashMap, FxHashSet};
 use rustc_data_structures::sync::{self, Lrc};
+use rustc_data_structures::unord::UnordSet;
 use rustc_errors::emitter::{Emitter, EmitterWriter};
 use rustc_errors::json::JsonEmitter;
 use rustc_feature::UnstableFeatures;
@@ -288,8 +289,7 @@ pub(crate) fn create_config(
             providers.typeck_item_bodies = |_, _| {};
             // hack so that `used_trait_imports` won't try to call typeck
             providers.used_trait_imports = |_, _| {
-                static EMPTY_SET: LazyLock<FxHashSet<LocalDefId>> =
-                    LazyLock::new(FxHashSet::default);
+                static EMPTY_SET: LazyLock<UnordSet<LocalDefId>> = LazyLock::new(UnordSet::default);
                 &EMPTY_SET
             };
             // In case typeck does end up being called, don't ICE in case there were name resolution errors