diff --git a/compiler/rustc_trait_selection/src/solve/eval_ctxt/canonical.rs b/compiler/rustc_trait_selection/src/solve/eval_ctxt/canonical.rs
index 9590a82c0677f..f6ec654908450 100644
--- a/compiler/rustc_trait_selection/src/solve/eval_ctxt/canonical.rs
+++ b/compiler/rustc_trait_selection/src/solve/eval_ctxt/canonical.rs
@@ -99,6 +99,13 @@ impl<'tcx> EvalCtxt<'_, InferCtxt<'tcx>> {
             previous call to `try_evaluate_added_goals!`"
         );
 
+        // We only check for leaks from universes which were entered inside
+        // of the query.
+        self.infcx.leak_check(self.max_input_universe, None).map_err(|e| {
+            trace!(?e, "failed the leak check");
+            NoSolution
+        })?;
+
         // When normalizing, we've replaced the expected term with an unconstrained
         // inference variable. This means that we dropped information which could
         // have been important. We handle this by instead returning the nested goals
@@ -121,7 +128,7 @@ impl<'tcx> EvalCtxt<'_, InferCtxt<'tcx>> {
         };
 
         let external_constraints =
-            self.compute_external_query_constraints(normalization_nested_goals)?;
+            self.compute_external_query_constraints(certainty, normalization_nested_goals);
         let (var_values, mut external_constraints) =
             (self.var_values, external_constraints).fold_with(&mut EagerResolver::new(self.infcx));
         // Remove any trivial region constraints once we've resolved regions
@@ -170,30 +177,37 @@ impl<'tcx> EvalCtxt<'_, InferCtxt<'tcx>> {
     #[instrument(level = "trace", skip(self), ret)]
     fn compute_external_query_constraints(
         &self,
+        certainty: Certainty,
         normalization_nested_goals: NestedNormalizationGoals<'tcx>,
-    ) -> Result<ExternalConstraintsData<'tcx>, NoSolution> {
-        // We only check for leaks from universes which were entered inside
-        // of the query.
-        self.infcx.leak_check(self.max_input_universe, None).map_err(|e| {
-            trace!(?e, "failed the leak check");
-            NoSolution
-        })?;
-
-        // Cannot use `take_registered_region_obligations` as we may compute the response
-        // inside of a `probe` whenever we have multiple choices inside of the solver.
-        let region_obligations = self.infcx.inner.borrow().region_obligations().to_owned();
-        let mut region_constraints = self.infcx.with_region_constraints(|region_constraints| {
-            make_query_region_constraints(
-                self.tcx(),
-                region_obligations
-                    .iter()
-                    .map(|r_o| (r_o.sup_type, r_o.sub_region, r_o.origin.to_constraint_category())),
-                region_constraints,
-            )
-        });
-
-        let mut seen = FxHashSet::default();
-        region_constraints.outlives.retain(|outlives| seen.insert(*outlives));
+    ) -> ExternalConstraintsData<'tcx> {
+        // We only return region constraints once the certainty is `Yes`. This
+        // is necessary as we may drop nested goals on ambiguity, which may result
+        // in unconstrained inference variables in the region constraints. It also
+        // prevents us from emitting duplicate region constraints, avoiding some
+        // unnecessary work. This slightly weakens the leak check in case it uses
+        // region constraints from an ambiguous nested goal. This is tested in both
+        // `tests/ui/higher-ranked/leak-check/leak-check-in-selection-5-ambig.rs` and
+        // `tests/ui/higher-ranked/leak-check/leak-check-in-selection-6-ambig-unify.rs`.
+        let region_constraints = if certainty == Certainty::Yes {
+            // Cannot use `take_registered_region_obligations` as we may compute the response
+            // inside of a `probe` whenever we have multiple choices inside of the solver.
+            let region_obligations = self.infcx.inner.borrow().region_obligations().to_owned();
+            let mut region_constraints = self.infcx.with_region_constraints(|region_constraints| {
+                make_query_region_constraints(
+                    self.tcx(),
+                    region_obligations.iter().map(|r_o| {
+                        (r_o.sup_type, r_o.sub_region, r_o.origin.to_constraint_category())
+                    }),
+                    region_constraints,
+                )
+            });
+
+            let mut seen = FxHashSet::default();
+            region_constraints.outlives.retain(|outlives| seen.insert(*outlives));
+            region_constraints
+        } else {
+            Default::default()
+        };
 
         let mut opaque_types = self.infcx.clone_opaque_types_for_query_response();
         // Only return opaque type keys for newly-defined opaques
@@ -201,7 +215,7 @@ impl<'tcx> EvalCtxt<'_, InferCtxt<'tcx>> {
             self.predefined_opaques_in_body.opaque_types.iter().all(|(pa, _)| pa != a)
         });
 
-        Ok(ExternalConstraintsData { region_constraints, opaque_types, normalization_nested_goals })
+        ExternalConstraintsData { region_constraints, opaque_types, normalization_nested_goals }
     }
 
     /// After calling a canonical query, we apply the constraints returned
diff --git a/tests/ui/higher-ranked/leak-check/leak-check-in-selection-5-ambig.rs b/tests/ui/higher-ranked/leak-check/leak-check-in-selection-5-ambig.rs
new file mode 100644
index 0000000000000..beda719ac208a
--- /dev/null
+++ b/tests/ui/higher-ranked/leak-check/leak-check-in-selection-5-ambig.rs
@@ -0,0 +1,28 @@
+//@ revisions: old next
+//@[next] compile-flags: -Znext-solver
+//@ check-pass
+
+// The new trait solver does not return region constraints if the goal
+// is still ambiguous. This causes the following test to fail with ambiguity,
+// even though `(): LeakCheckFailure<'!a, V>` would return `'!a: 'static`
+// which would have caused a leak check failure.
+
+trait Ambig {}
+impl Ambig for u32 {}
+impl Ambig for u16 {}
+
+trait Id<T> {}
+impl Id<u32> for u32 {}
+impl Id<u16> for u16 {}
+
+
+trait LeakCheckFailure<'a, V: ?Sized> {}
+impl<V: ?Sized + Ambig> LeakCheckFailure<'static, V> for () {}
+
+trait Trait<U, V> {}
+impl<V> Trait<u32, V> for () where for<'a> (): LeakCheckFailure<'a, V> {}
+impl<V> Trait<u16, V> for () {}
+fn impls_trait<T: Trait<U, V>, U: Id<V>, V>() {}
+fn main() {
+    impls_trait::<(), _, _>()
+}
diff --git a/tests/ui/higher-ranked/leak-check/leak-check-in-selection-6-ambig-unify.next.stderr b/tests/ui/higher-ranked/leak-check/leak-check-in-selection-6-ambig-unify.next.stderr
new file mode 100644
index 0000000000000..a12e3312230af
--- /dev/null
+++ b/tests/ui/higher-ranked/leak-check/leak-check-in-selection-6-ambig-unify.next.stderr
@@ -0,0 +1,22 @@
+error[E0283]: type annotations needed
+  --> $DIR/leak-check-in-selection-6-ambig-unify.rs:30:5
+   |
+LL |     impls_trait::<(), _, _>()
+   |     ^^^^^^^^^^^^^^^^^^^^^^^ cannot infer type of the type parameter `U` declared on the function `impls_trait`
+   |
+note: multiple `impl`s satisfying `(): Trait<_, _>` found
+  --> $DIR/leak-check-in-selection-6-ambig-unify.rs:26:1
+   |
+LL | impl<V> Trait<u32, V> for () where for<'b> (): LeakCheckFailure<'static, 'b, V> {}
+   | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+LL | impl<V> Trait<u16, V> for () {}
+   | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+note: required by a bound in `impls_trait`
+  --> $DIR/leak-check-in-selection-6-ambig-unify.rs:28:19
+   |
+LL | fn impls_trait<T: Trait<U, V>, U: Id<V>, V>() {}
+   |                   ^^^^^^^^^^^ required by this bound in `impls_trait`
+
+error: aborting due to 1 previous error
+
+For more information about this error, try `rustc --explain E0283`.
diff --git a/tests/ui/higher-ranked/leak-check/leak-check-in-selection-6-ambig-unify.old.stderr b/tests/ui/higher-ranked/leak-check/leak-check-in-selection-6-ambig-unify.old.stderr
new file mode 100644
index 0000000000000..a12e3312230af
--- /dev/null
+++ b/tests/ui/higher-ranked/leak-check/leak-check-in-selection-6-ambig-unify.old.stderr
@@ -0,0 +1,22 @@
+error[E0283]: type annotations needed
+  --> $DIR/leak-check-in-selection-6-ambig-unify.rs:30:5
+   |
+LL |     impls_trait::<(), _, _>()
+   |     ^^^^^^^^^^^^^^^^^^^^^^^ cannot infer type of the type parameter `U` declared on the function `impls_trait`
+   |
+note: multiple `impl`s satisfying `(): Trait<_, _>` found
+  --> $DIR/leak-check-in-selection-6-ambig-unify.rs:26:1
+   |
+LL | impl<V> Trait<u32, V> for () where for<'b> (): LeakCheckFailure<'static, 'b, V> {}
+   | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+LL | impl<V> Trait<u16, V> for () {}
+   | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+note: required by a bound in `impls_trait`
+  --> $DIR/leak-check-in-selection-6-ambig-unify.rs:28:19
+   |
+LL | fn impls_trait<T: Trait<U, V>, U: Id<V>, V>() {}
+   |                   ^^^^^^^^^^^ required by this bound in `impls_trait`
+
+error: aborting due to 1 previous error
+
+For more information about this error, try `rustc --explain E0283`.
diff --git a/tests/ui/higher-ranked/leak-check/leak-check-in-selection-6-ambig-unify.rs b/tests/ui/higher-ranked/leak-check/leak-check-in-selection-6-ambig-unify.rs
new file mode 100644
index 0000000000000..592d581695e52
--- /dev/null
+++ b/tests/ui/higher-ranked/leak-check/leak-check-in-selection-6-ambig-unify.rs
@@ -0,0 +1,32 @@
+//@ revisions: old next
+//@[next] compile-flags: -Znext-solver
+
+// The new trait solver does not return region constraints if the goal
+// is still ambiguous. This should cause the following test to fail with
+// ambiguity as even if  `(): LeakCheckFailure<'static, '!b, V>` unifies
+// `'!b` with `'static`, we erase all region constraints.
+//
+// However, we do still unify the var_value for `'b` with `'static`,
+// causing us to return this requirement via the `var_values` even if
+// we don't return any region constraints. This is a bit inconsistent
+// but isn't something we should really worry about imo.
+trait Ambig {}
+impl Ambig for u32 {}
+impl Ambig for u16 {}
+
+trait Id<T> {}
+impl Id<u32> for u32 {}
+impl Id<u16> for u16 {}
+
+
+trait LeakCheckFailure<'a, 'b, V: ?Sized> {}
+impl<'a, 'b: 'a, V: ?Sized + Ambig> LeakCheckFailure<'a, 'b, V> for () {}
+
+trait Trait<U, V> {}
+impl<V> Trait<u32, V> for () where for<'b> (): LeakCheckFailure<'static, 'b, V> {}
+impl<V> Trait<u16, V> for () {}
+fn impls_trait<T: Trait<U, V>, U: Id<V>, V>() {}
+fn main() {
+    impls_trait::<(), _, _>()
+    //~^ ERROR type annotations needed
+}
diff --git a/tests/ui/traits/next-solver/normalize/ambig-goal-infer-in-type-oulives.rs b/tests/ui/traits/next-solver/normalize/ambig-goal-infer-in-type-oulives.rs
new file mode 100644
index 0000000000000..18dc34f7cc437
--- /dev/null
+++ b/tests/ui/traits/next-solver/normalize/ambig-goal-infer-in-type-oulives.rs
@@ -0,0 +1,29 @@
+//@ check-pass
+//@ compile-flags: -Znext-solver
+//@ ignore-compare-mode-next-solver (explicitly enabled)
+
+// Regression test for an ICE when trying to bootstrap rustc
+// with #125343. An ambiguous goal returned a `TypeOutlives`
+// constraint referencing an inference variable. This inference
+// variable was created inside of the goal, causing it to be
+// unconstrained in the caller. This then caused an ICE in MIR
+// borrowck.
+
+struct Foo<T>(T);
+trait Extend<T> {
+    fn extend<I: IntoIterator<Item = T>>(iter: I);
+}
+
+impl<T> Extend<T> for Foo<T> {
+    fn extend<I: IntoIterator<Item = T>>(_: I) {
+        todo!()
+    }
+}
+
+impl<'a, T: 'a + Copy> Extend<&'a T> for Foo<T> {
+    fn extend<I: IntoIterator<Item = &'a T>>(iter: I) {
+        <Self as Extend<T>>::extend(iter.into_iter().copied())
+    }
+}
+
+fn main() {}