diff --git a/compiler/rustc_hir_analysis/src/coherence/inherent_impls_overlap.rs b/compiler/rustc_hir_analysis/src/coherence/inherent_impls_overlap.rs
index c634a57b0b534..130eb8005b069 100644
--- a/compiler/rustc_hir_analysis/src/coherence/inherent_impls_overlap.rs
+++ b/compiler/rustc_hir_analysis/src/coherence/inherent_impls_overlap.rs
@@ -148,12 +148,11 @@ impl<'tcx> InherentOverlapChecker<'tcx> {
             // inherent impls without warning.
             SkipLeakCheck::Yes,
             overlap_mode,
-            |overlap| {
-                self.check_for_common_items_in_impls(impl1_def_id, impl2_def_id, overlap);
-                false
-            },
-            || true,
-        );
+        )
+        .map_or(true, |overlap| {
+            self.check_for_common_items_in_impls(impl1_def_id, impl2_def_id, overlap);
+            false
+        });
     }
 
     fn check_item(&mut self, id: hir::ItemId) {
diff --git a/compiler/rustc_trait_selection/src/traits/coherence.rs b/compiler/rustc_trait_selection/src/traits/coherence.rs
index 7715874743192..8aab75490a81b 100644
--- a/compiler/rustc_trait_selection/src/traits/coherence.rs
+++ b/compiler/rustc_trait_selection/src/traits/coherence.rs
@@ -60,23 +60,17 @@ pub fn add_placeholder_note(err: &mut Diagnostic) {
     );
 }
 
-/// If there are types that satisfy both impls, invokes `on_overlap`
+/// If there are types that satisfy both impls, returns `Some`
 /// with a suitably-freshened `ImplHeader` with those types
-/// substituted. Otherwise, invokes `no_overlap`.
-#[instrument(skip(tcx, skip_leak_check, on_overlap, no_overlap), level = "debug")]
-pub fn overlapping_impls<F1, F2, R>(
+/// substituted. Otherwise, returns `None`.
+#[instrument(skip(tcx, skip_leak_check), level = "debug")]
+pub fn overlapping_impls(
     tcx: TyCtxt<'_>,
     impl1_def_id: DefId,
     impl2_def_id: DefId,
     skip_leak_check: SkipLeakCheck,
     overlap_mode: OverlapMode,
-    on_overlap: F1,
-    no_overlap: F2,
-) -> R
-where
-    F1: FnOnce(OverlapResult<'_>) -> R,
-    F2: FnOnce() -> R,
-{
+) -> Option<OverlapResult<'_>> {
     // Before doing expensive operations like entering an inference context, do
     // a quick check via fast_reject to tell if the impl headers could possibly
     // unify.
@@ -97,7 +91,7 @@ where
     if !may_overlap {
         // Some types involved are definitely different, so the impls couldn't possibly overlap.
         debug!("overlapping_impls: fast_reject early-exit");
-        return no_overlap();
+        return None;
     }
 
     let infcx = tcx.infer_ctxt().build();
@@ -105,7 +99,7 @@ where
     let overlaps =
         overlap(selcx, skip_leak_check, impl1_def_id, impl2_def_id, overlap_mode).is_some();
     if !overlaps {
-        return no_overlap();
+        return None;
     }
 
     // In the case where we detect an error, run the check again, but
@@ -114,7 +108,7 @@ where
     let infcx = tcx.infer_ctxt().build();
     let selcx = &mut SelectionContext::intercrate(&infcx);
     selcx.enable_tracking_intercrate_ambiguity_causes();
-    on_overlap(overlap(selcx, skip_leak_check, impl1_def_id, impl2_def_id, overlap_mode).unwrap())
+    Some(overlap(selcx, skip_leak_check, impl1_def_id, impl2_def_id, overlap_mode).unwrap())
 }
 
 fn with_fresh_ty_vars<'cx, 'tcx>(
diff --git a/compiler/rustc_trait_selection/src/traits/specialize/specialization_graph.rs b/compiler/rustc_trait_selection/src/traits/specialize/specialization_graph.rs
index fcb73b43fa8a1..63f89a33e8adc 100644
--- a/compiler/rustc_trait_selection/src/traits/specialize/specialization_graph.rs
+++ b/compiler/rustc_trait_selection/src/traits/specialize/specialization_graph.rs
@@ -137,9 +137,8 @@ impl ChildrenExt<'_> for Children {
                     impl_def_id,
                     traits::SkipLeakCheck::default(),
                     overlap_mode,
-                    |_| true,
-                    || false,
-                );
+                )
+                .is_some();
 
                 let error = create_overlap_error(overlap);
 
@@ -162,34 +161,29 @@ impl ChildrenExt<'_> for Children {
                 impl_def_id,
                 traits::SkipLeakCheck::Yes,
                 overlap_mode,
-                |overlap| {
-                    if let Some(overlap_kind) =
-                        tcx.impls_are_allowed_to_overlap(impl_def_id, possible_sibling)
-                    {
-                        match overlap_kind {
-                            ty::ImplOverlapKind::Permitted { marker: _ } => {}
-                            ty::ImplOverlapKind::Issue33140 => {
-                                *last_lint_mut = Some(FutureCompatOverlapError {
-                                    error: create_overlap_error(overlap),
-                                    kind: FutureCompatOverlapErrorKind::Issue33140,
-                                });
-                            }
+            )
+            .map_or(Ok((false, false)), |overlap| {
+                if let Some(overlap_kind) =
+                    tcx.impls_are_allowed_to_overlap(impl_def_id, possible_sibling)
+                {
+                    match overlap_kind {
+                        ty::ImplOverlapKind::Permitted { marker: _ } => {}
+                        ty::ImplOverlapKind::Issue33140 => {
+                            *last_lint_mut = Some(FutureCompatOverlapError {
+                                error: create_overlap_error(overlap),
+                                kind: FutureCompatOverlapErrorKind::Issue33140,
+                            });
                         }
-
-                        return Ok((false, false));
                     }
 
-                    let le = tcx.specializes((impl_def_id, possible_sibling));
-                    let ge = tcx.specializes((possible_sibling, impl_def_id));
+                    return Ok((false, false));
+                }
 
-                    if le == ge {
-                        report_overlap_error(overlap, last_lint_mut)
-                    } else {
-                        Ok((le, ge))
-                    }
-                },
-                || Ok((false, false)),
-            )?;
+                let le = tcx.specializes((impl_def_id, possible_sibling));
+                let ge = tcx.specializes((possible_sibling, impl_def_id));
+
+                if le == ge { report_overlap_error(overlap, last_lint_mut) } else { Ok((le, ge)) }
+            })?;
 
             if le && !ge {
                 debug!(