diff --git a/compiler/rustc_trait_selection/src/solve/eval_ctxt/mod.rs b/compiler/rustc_trait_selection/src/solve/eval_ctxt/mod.rs
index a0fe6eca0fc..5d9b588b55b 100644
--- a/compiler/rustc_trait_selection/src/solve/eval_ctxt/mod.rs
+++ b/compiler/rustc_trait_selection/src/solve/eval_ctxt/mod.rs
@@ -720,7 +720,8 @@ impl<'tcx> EvalCtxt<'_, 'tcx> {
     ) -> Result<(), NoSolution> {
         self.infcx
             .at(&ObligationCause::dummy(), param_env)
-            .eq(DefineOpaqueTypes::No, lhs, rhs)
+            // New solver ignores DefineOpaqueTypes, so choose Yes for consistency
+            .eq(DefineOpaqueTypes::Yes, lhs, rhs)
             .map(|InferOk { value: (), obligations }| {
                 self.add_goals(GoalSource::Misc, obligations.into_iter().map(|o| o.into()));
             })
@@ -759,7 +760,8 @@ impl<'tcx> EvalCtxt<'_, 'tcx> {
     ) -> Result<(), NoSolution> {
         self.infcx
             .at(&ObligationCause::dummy(), param_env)
-            .sub(DefineOpaqueTypes::No, sub, sup)
+            // New solver ignores DefineOpaqueTypes, so choose Yes for consistency
+            .sub(DefineOpaqueTypes::Yes, sub, sup)
             .map(|InferOk { value: (), obligations }| {
                 self.add_goals(GoalSource::Misc, obligations.into_iter().map(|o| o.into()));
             })
@@ -779,7 +781,8 @@ impl<'tcx> EvalCtxt<'_, 'tcx> {
     ) -> Result<(), NoSolution> {
         self.infcx
             .at(&ObligationCause::dummy(), param_env)
-            .relate(DefineOpaqueTypes::No, lhs, variance, rhs)
+            // New solver ignores DefineOpaqueTypes, so choose Yes for consistency
+            .relate(DefineOpaqueTypes::Yes, lhs, variance, rhs)
             .map(|InferOk { value: (), obligations }| {
                 self.add_goals(GoalSource::Misc, obligations.into_iter().map(|o| o.into()));
             })
@@ -803,7 +806,8 @@ impl<'tcx> EvalCtxt<'_, 'tcx> {
     ) -> Result<Vec<Goal<'tcx, ty::Predicate<'tcx>>>, NoSolution> {
         self.infcx
             .at(&ObligationCause::dummy(), param_env)
-            .eq(DefineOpaqueTypes::No, lhs, rhs)
+            // New solver ignores DefineOpaqueTypes, so choose Yes for consistency
+            .eq(DefineOpaqueTypes::Yes, lhs, rhs)
             .map(|InferOk { value: (), obligations }| {
                 obligations.into_iter().map(|o| o.into()).collect()
             })
diff --git a/compiler/rustc_trait_selection/src/solve/eval_ctxt/select.rs b/compiler/rustc_trait_selection/src/solve/eval_ctxt/select.rs
index e0c7804b6db..6644d3c77af 100644
--- a/compiler/rustc_trait_selection/src/solve/eval_ctxt/select.rs
+++ b/compiler/rustc_trait_selection/src/solve/eval_ctxt/select.rs
@@ -182,7 +182,8 @@ fn rematch_impl<'tcx>(
 
     let mut nested = infcx
         .at(&ObligationCause::dummy(), goal.param_env)
-        .eq(DefineOpaqueTypes::No, goal.predicate.trait_ref, impl_trait_ref)
+        // New solver ignores DefineOpaqueTypes, so choose Yes for consistency
+        .eq(DefineOpaqueTypes::Yes, goal.predicate.trait_ref, impl_trait_ref)
         .map_err(|_| SelectionError::Unimplemented)?
         .into_obligations();
 
@@ -257,7 +258,8 @@ fn rematch_unsize<'tcx>(
             nested.extend(
                 infcx
                     .at(&ObligationCause::dummy(), goal.param_env)
-                    .eq(DefineOpaqueTypes::No, a_elem_ty, b_elem_ty)
+                    // New solver ignores DefineOpaqueTypes, so choose Yes for consistency
+                    .eq(DefineOpaqueTypes::Yes, a_elem_ty, b_elem_ty)
                     .expect("expected rematch to succeed")
                     .into_obligations(),
             );
@@ -300,7 +302,8 @@ fn rematch_unsize<'tcx>(
             nested.extend(
                 infcx
                     .at(&ObligationCause::dummy(), goal.param_env)
-                    .eq(DefineOpaqueTypes::No, unsized_a_ty, b_ty)
+                    // New solver ignores DefineOpaqueTypes, so choose Yes for consistency
+                    .eq(DefineOpaqueTypes::Yes, unsized_a_ty, b_ty)
                     .expect("expected rematch to succeed")
                     .into_obligations(),
             );
@@ -329,7 +332,8 @@ fn rematch_unsize<'tcx>(
             nested.extend(
                 infcx
                     .at(&ObligationCause::dummy(), goal.param_env)
-                    .eq(DefineOpaqueTypes::No, unsized_a_ty, b_ty)
+                    // New solver ignores DefineOpaqueTypes, so choose Yes for consistency
+                    .eq(DefineOpaqueTypes::Yes, unsized_a_ty, b_ty)
                     .expect("expected rematch to succeed")
                     .into_obligations(),
             );
diff --git a/compiler/rustc_trait_selection/src/traits/coherence.rs b/compiler/rustc_trait_selection/src/traits/coherence.rs
index 90e337a53b6..8625ad378f7 100644
--- a/compiler/rustc_trait_selection/src/traits/coherence.rs
+++ b/compiler/rustc_trait_selection/src/traits/coherence.rs
@@ -477,7 +477,8 @@ fn plug_infer_with_placeholders<'tcx>(
             if ty.is_ty_var() {
                 let Ok(InferOk { value: (), obligations }) =
                     self.infcx.at(&ObligationCause::dummy(), ty::ParamEnv::empty()).eq(
-                        DefineOpaqueTypes::No,
+                        // Comparing against a type variable never registers hidden types anyway
+                        DefineOpaqueTypes::Yes,
                         ty,
                         Ty::new_placeholder(
                             self.infcx.tcx,
@@ -504,7 +505,9 @@ fn plug_infer_with_placeholders<'tcx>(
             if ct.is_ct_infer() {
                 let Ok(InferOk { value: (), obligations }) =
                     self.infcx.at(&ObligationCause::dummy(), ty::ParamEnv::empty()).eq(
-                        DefineOpaqueTypes::No,
+                        // The types of the constants are the same, so there is no hidden type
+                        // registration happening anyway.
+                        DefineOpaqueTypes::Yes,
                         ct,
                         ty::Const::new_placeholder(
                             self.infcx.tcx,
@@ -532,7 +535,8 @@ fn plug_infer_with_placeholders<'tcx>(
                 if r.is_var() {
                     let Ok(InferOk { value: (), obligations }) =
                         self.infcx.at(&ObligationCause::dummy(), ty::ParamEnv::empty()).eq(
-                            DefineOpaqueTypes::No,
+                            // Lifetimes don't contain opaque types (or any types for that matter).
+                            DefineOpaqueTypes::Yes,
                             r,
                             ty::Region::new_placeholder(
                                 self.infcx.tcx,