diff --git a/compiler/rustc_index/src/bit_set.rs b/compiler/rustc_index/src/bit_set.rs
index 0b501da7cd975..100824f4b9448 100644
--- a/compiler/rustc_index/src/bit_set.rs
+++ b/compiler/rustc_index/src/bit_set.rs
@@ -707,6 +707,18 @@ impl<T: Idx> GrowableBitSet<T> {
         self.bit_set.insert(elem)
     }
 
+    /// Returns `true` if the set has changed.
+    #[inline]
+    pub fn remove(&mut self, elem: T) -> bool {
+        self.ensure(elem.index() + 1);
+        self.bit_set.remove(elem)
+    }
+
+    #[inline]
+    pub fn is_empty(&self) -> bool {
+        self.bit_set.is_empty()
+    }
+
     #[inline]
     pub fn contains(&self, elem: T) -> bool {
         let (word_index, mask) = word_index_and_mask(elem);
diff --git a/compiler/rustc_trait_selection/src/traits/select/confirmation.rs b/compiler/rustc_trait_selection/src/traits/select/confirmation.rs
index 3015188fd447a..3e3e945f654b7 100644
--- a/compiler/rustc_trait_selection/src/traits/select/confirmation.rs
+++ b/compiler/rustc_trait_selection/src/traits/select/confirmation.rs
@@ -829,16 +829,11 @@ impl<'cx, 'tcx> SelectionContext<'cx, 'tcx> {
                 let tail_field_ty = tcx.type_of(tail_field.did);
 
                 let mut unsizing_params = GrowableBitSet::new_empty();
-                let mut found = false;
                 for arg in tail_field_ty.walk() {
                     if let Some(i) = maybe_unsizing_param_idx(arg) {
                         unsizing_params.insert(i);
-                        found = true;
                     }
                 }
-                if !found {
-                    return Err(Unimplemented);
-                }
 
                 // Ensure none of the other fields mention the parameters used
                 // in unsizing.
@@ -848,13 +843,15 @@ impl<'cx, 'tcx> SelectionContext<'cx, 'tcx> {
                 for field in prefix_fields {
                     for arg in tcx.type_of(field.did).walk() {
                         if let Some(i) = maybe_unsizing_param_idx(arg) {
-                            if unsizing_params.contains(i) {
-                                return Err(Unimplemented);
-                            }
+                            unsizing_params.remove(i);
                         }
                     }
                 }
 
+                if unsizing_params.is_empty() {
+                    return Err(Unimplemented);
+                }
+
                 // Extract `TailField<T>` and `TailField<U>` from `Struct<T>` and `Struct<U>`.
                 let source_tail = tail_field_ty.subst(tcx, substs_a);
                 let target_tail = tail_field_ty.subst(tcx, substs_b);
diff --git a/src/test/ui/unsized/unchanged-param.rs b/src/test/ui/unsized/unchanged-param.rs
new file mode 100644
index 0000000000000..93c7af68ac388
--- /dev/null
+++ b/src/test/ui/unsized/unchanged-param.rs
@@ -0,0 +1,11 @@
+// run-pass
+// Test that we allow unsizing even if there is an unchanged param in the
+// field getting unsized.
+struct A<T, U: ?Sized + 'static>(T, B<T, U>);
+struct B<T, U: ?Sized>(T, U);
+
+fn main() {
+    let x: A<[u32; 1], [u32; 1]> = A([0; 1], B([0; 1], [0; 1]));
+    let y: &A<[u32; 1], [u32]> = &x;
+    assert_eq!(y.1.1.len(), 1);
+}