diff --git a/compiler/rustc_middle/src/ty/sty.rs b/compiler/rustc_middle/src/ty/sty.rs
index d9a65ae57a0..9984fb085ef 100644
--- a/compiler/rustc_middle/src/ty/sty.rs
+++ b/compiler/rustc_middle/src/ty/sty.rs
@@ -1873,14 +1873,14 @@ impl<'tcx> Ty<'tcx> {
 
     /// Fast path helper for testing if a type is `Sized`.
     ///
-    /// Returning true means the type is known to be sized. Returning
-    /// `false` means nothing -- could be sized, might not be.
+    /// Returning true means the type is known to implement `Sized`. Returning `false` means
+    /// nothing -- could be sized, might not be.
     ///
-    /// Note that we could never rely on the fact that a type such as `[_]` is
-    /// trivially `!Sized` because we could be in a type environment with a
-    /// bound such as `[_]: Copy`. A function with such a bound obviously never
-    /// can be called, but that doesn't mean it shouldn't typecheck. This is why
-    /// this method doesn't return `Option<bool>`.
+    /// Note that we could never rely on the fact that a type such as `[_]` is trivially `!Sized`
+    /// because we could be in a type environment with a bound such as `[_]: Copy`. A function with
+    /// such a bound obviously never can be called, but that doesn't mean it shouldn't typecheck.
+    /// This is why this method doesn't return `Option<bool>`.
+    #[instrument(skip(tcx), level = "debug")]
     pub fn is_trivially_sized(self, tcx: TyCtxt<'tcx>) -> bool {
         match self.kind() {
             ty::Infer(ty::IntVar(_) | ty::FloatVar(_))
diff --git a/compiler/rustc_trait_selection/src/traits/fulfill.rs b/compiler/rustc_trait_selection/src/traits/fulfill.rs
index e98a240a53f..1b76d48e431 100644
--- a/compiler/rustc_trait_selection/src/traits/fulfill.rs
+++ b/compiler/rustc_trait_selection/src/traits/fulfill.rs
@@ -24,10 +24,10 @@ use super::{
 };
 use crate::error_reporting::InferCtxtErrorExt;
 use crate::infer::{InferCtxt, TyOrConstInferVar};
-use crate::traits::EvaluateConstErr;
 use crate::traits::normalize::normalize_with_depth_to;
 use crate::traits::project::{PolyProjectionObligation, ProjectionCacheKeyExt as _};
 use crate::traits::query::evaluate_obligation::InferCtxtExt;
+use crate::traits::{EvaluateConstErr, sizedness_fast_path};
 
 pub(crate) type PendingPredicateObligations<'tcx> = ThinVec<PendingPredicateObligation<'tcx>>;
 
@@ -335,6 +335,10 @@ impl<'a, 'tcx> ObligationProcessor for FulfillProcessor<'a, 'tcx> {
 
         let infcx = self.selcx.infcx;
 
+        if sizedness_fast_path(infcx.tcx, obligation.predicate) {
+            return ProcessResult::Changed(thin_vec::thin_vec![]);
+        }
+
         if obligation.predicate.has_aliases() {
             let mut obligations = PredicateObligations::new();
             let predicate = normalize_with_depth_to(
diff --git a/compiler/rustc_trait_selection/src/traits/mod.rs b/compiler/rustc_trait_selection/src/traits/mod.rs
index de337710b5e..f2713b98f0a 100644
--- a/compiler/rustc_trait_selection/src/traits/mod.rs
+++ b/compiler/rustc_trait_selection/src/traits/mod.rs
@@ -65,8 +65,8 @@ pub use self::specialize::{
 pub use self::structural_normalize::StructurallyNormalizeExt;
 pub use self::util::{
     BoundVarReplacer, PlaceholderReplacer, elaborate, expand_trait_aliases, impl_item_is_final,
-    supertrait_def_ids, supertraits, transitive_bounds_that_define_assoc_item, upcast_choices,
-    with_replaced_escaping_bound_vars,
+    sizedness_fast_path, supertrait_def_ids, supertraits, transitive_bounds_that_define_assoc_item,
+    upcast_choices, with_replaced_escaping_bound_vars,
 };
 use crate::error_reporting::InferCtxtErrorExt;
 use crate::infer::outlives::env::OutlivesEnvironment;
diff --git a/compiler/rustc_trait_selection/src/traits/query/type_op/prove_predicate.rs b/compiler/rustc_trait_selection/src/traits/query/type_op/prove_predicate.rs
index 4f9e2e79d62..87fc532adaf 100644
--- a/compiler/rustc_trait_selection/src/traits/query/type_op/prove_predicate.rs
+++ b/compiler/rustc_trait_selection/src/traits/query/type_op/prove_predicate.rs
@@ -1,4 +1,3 @@
-use rustc_hir::LangItem;
 use rustc_infer::traits::Obligation;
 use rustc_middle::traits::ObligationCause;
 use rustc_middle::traits::query::NoSolution;
@@ -7,7 +6,7 @@ use rustc_middle::ty::{self, ParamEnvAnd, TyCtxt};
 use rustc_span::Span;
 
 use crate::infer::canonical::{CanonicalQueryInput, CanonicalQueryResponse};
-use crate::traits::ObligationCtxt;
+use crate::traits::{ObligationCtxt, sizedness_fast_path};
 
 impl<'tcx> super::QueryTypeOp<'tcx> for ProvePredicate<'tcx> {
     type QueryResponse = ();
@@ -16,15 +15,7 @@ impl<'tcx> super::QueryTypeOp<'tcx> for ProvePredicate<'tcx> {
         tcx: TyCtxt<'tcx>,
         key: &ParamEnvAnd<'tcx, Self>,
     ) -> Option<Self::QueryResponse> {
-        // Proving Sized, very often on "obviously sized" types like
-        // `&T`, accounts for about 60% percentage of the predicates
-        // we have to prove. No need to canonicalize and all that for
-        // such cases.
-        if let ty::PredicateKind::Clause(ty::ClauseKind::Trait(trait_ref)) =
-            key.value.predicate.kind().skip_binder()
-            && tcx.is_lang_item(trait_ref.def_id(), LangItem::Sized)
-            && trait_ref.self_ty().is_trivially_sized(tcx)
-        {
+        if sizedness_fast_path(tcx, key.value.predicate) {
             return Some(());
         }
 
diff --git a/compiler/rustc_trait_selection/src/traits/select/mod.rs b/compiler/rustc_trait_selection/src/traits/select/mod.rs
index 56ff46e89e7..4d88a23250a 100644
--- a/compiler/rustc_trait_selection/src/traits/select/mod.rs
+++ b/compiler/rustc_trait_selection/src/traits/select/mod.rs
@@ -49,7 +49,9 @@ use crate::infer::{InferCtxt, InferOk, TypeFreshener};
 use crate::solve::InferCtxtSelectExt as _;
 use crate::traits::normalize::{normalize_with_depth, normalize_with_depth_to};
 use crate::traits::project::{ProjectAndUnifyResult, ProjectionCacheKeyExt};
-use crate::traits::{EvaluateConstErr, ProjectionCacheKey, Unimplemented, effects};
+use crate::traits::{
+    EvaluateConstErr, ProjectionCacheKey, Unimplemented, effects, sizedness_fast_path,
+};
 
 mod _match;
 mod candidate_assembly;
@@ -603,6 +605,10 @@ impl<'cx, 'tcx> SelectionContext<'cx, 'tcx> {
             None => self.check_recursion_limit(&obligation, &obligation)?,
         }
 
+        if sizedness_fast_path(self.tcx(), obligation.predicate) {
+            return Ok(EvaluatedToOk);
+        }
+
         ensure_sufficient_stack(|| {
             let bound_predicate = obligation.predicate.kind();
             match bound_predicate.skip_binder() {
diff --git a/compiler/rustc_trait_selection/src/traits/util.rs b/compiler/rustc_trait_selection/src/traits/util.rs
index 9f20cd7eacb..035fd38c48a 100644
--- a/compiler/rustc_trait_selection/src/traits/util.rs
+++ b/compiler/rustc_trait_selection/src/traits/util.rs
@@ -1,6 +1,7 @@
 use std::collections::{BTreeMap, VecDeque};
 
 use rustc_data_structures::fx::{FxHashSet, FxIndexMap};
+use rustc_hir::LangItem;
 use rustc_hir::def_id::DefId;
 use rustc_infer::infer::InferCtxt;
 pub use rustc_infer::traits::util::*;
@@ -504,3 +505,21 @@ impl<'tcx> TypeFolder<TyCtxt<'tcx>> for PlaceholderReplacer<'_, 'tcx> {
         }
     }
 }
+
+pub fn sizedness_fast_path<'tcx>(tcx: TyCtxt<'tcx>, predicate: ty::Predicate<'tcx>) -> bool {
+    // Proving `Sized` very often on "obviously sized" types like `&T`, accounts for about 60%
+    // percentage of the predicates we have to prove. No need to canonicalize and all that for
+    // such cases.
+    if let ty::PredicateKind::Clause(ty::ClauseKind::Trait(trait_ref)) =
+        predicate.kind().skip_binder()
+    {
+        if tcx.is_lang_item(trait_ref.def_id(), LangItem::Sized)
+            && trait_ref.self_ty().is_trivially_sized(tcx)
+        {
+            debug!("fast path -- trivial sizedness");
+            return true;
+        }
+    }
+
+    false
+}
diff --git a/compiler/rustc_traits/src/codegen.rs b/compiler/rustc_traits/src/codegen.rs
index 4a889abfc28..88f02d16c7d 100644
--- a/compiler/rustc_traits/src/codegen.rs
+++ b/compiler/rustc_traits/src/codegen.rs
@@ -6,11 +6,11 @@
 use rustc_infer::infer::TyCtxtInferExt;
 use rustc_middle::bug;
 use rustc_middle::traits::CodegenObligationError;
-use rustc_middle::ty::{self, PseudoCanonicalInput, TyCtxt, TypeVisitableExt};
+use rustc_middle::ty::{self, PseudoCanonicalInput, TyCtxt, TypeVisitableExt, Upcast};
 use rustc_trait_selection::error_reporting::InferCtxtErrorExt;
 use rustc_trait_selection::traits::{
     ImplSource, Obligation, ObligationCause, ObligationCtxt, ScrubbedTraitError, SelectionContext,
-    Unimplemented,
+    Unimplemented, sizedness_fast_path,
 };
 use tracing::debug;
 
@@ -34,6 +34,13 @@ pub(crate) fn codegen_select_candidate<'tcx>(
     let (infcx, param_env) = tcx.infer_ctxt().ignoring_regions().build_with_typing_env(typing_env);
     let mut selcx = SelectionContext::new(&infcx);
 
+    if sizedness_fast_path(tcx, trait_ref.upcast(tcx)) {
+        return Ok(&*tcx.arena.alloc(ImplSource::Builtin(
+            ty::solve::BuiltinImplSource::Trivial,
+            Default::default(),
+        )));
+    }
+
     let obligation_cause = ObligationCause::dummy();
     let obligation = Obligation::new(tcx, obligation_cause, param_env, trait_ref);
 
diff --git a/compiler/rustc_traits/src/evaluate_obligation.rs b/compiler/rustc_traits/src/evaluate_obligation.rs
index c9ad096c6e9..7771db855d7 100644
--- a/compiler/rustc_traits/src/evaluate_obligation.rs
+++ b/compiler/rustc_traits/src/evaluate_obligation.rs
@@ -5,6 +5,7 @@ use rustc_span::DUMMY_SP;
 use rustc_trait_selection::traits::query::CanonicalPredicateGoal;
 use rustc_trait_selection::traits::{
     EvaluationResult, Obligation, ObligationCause, OverflowError, SelectionContext, TraitQueryMode,
+    sizedness_fast_path,
 };
 use tracing::debug;
 
@@ -23,6 +24,10 @@ fn evaluate_obligation<'tcx>(
     debug!("evaluate_obligation: goal={:#?}", goal);
     let ParamEnvAnd { param_env, value: predicate } = goal;
 
+    if sizedness_fast_path(tcx, predicate) {
+        return Ok(EvaluationResult::EvaluatedToOk);
+    }
+
     let mut selcx = SelectionContext::with_query_mode(infcx, TraitQueryMode::Canonical);
     let obligation = Obligation::new(tcx, ObligationCause::dummy(), param_env, predicate);
 
diff --git a/tests/ui/closures/issue-78720.rs b/tests/ui/closures/issue-78720.rs
index 81af030fe55..a615cdf2690 100644
--- a/tests/ui/closures/issue-78720.rs
+++ b/tests/ui/closures/issue-78720.rs
@@ -1,5 +1,6 @@
 fn server() -> impl {
     //~^ ERROR at least one trait must be specified
+    //~^^ ERROR type annotations needed
     ().map2(|| "")
 }
 
diff --git a/tests/ui/closures/issue-78720.stderr b/tests/ui/closures/issue-78720.stderr
index 90672cd83d7..3e95fab441a 100644
--- a/tests/ui/closures/issue-78720.stderr
+++ b/tests/ui/closures/issue-78720.stderr
@@ -5,7 +5,7 @@ LL | fn server() -> impl {
    |                ^^^^
 
 error[E0412]: cannot find type `F` in this scope
-  --> $DIR/issue-78720.rs:13:12
+  --> $DIR/issue-78720.rs:14:12
    |
 LL |     _func: F,
    |            ^
@@ -22,8 +22,14 @@ help: you might be missing a type parameter
 LL | struct Map2<Segment2, F> {
    |                     +++
 
+error[E0282]: type annotations needed
+  --> $DIR/issue-78720.rs:1:16
+   |
+LL | fn server() -> impl {
+   |                ^^^^ cannot infer type
+
 error[E0308]: mismatched types
-  --> $DIR/issue-78720.rs:7:39
+  --> $DIR/issue-78720.rs:8:39
    |
 LL |     fn map2<F>(self, f: F) -> Map2<F> {}
    |                                       ^^ expected `Map2<F>`, found `()`
@@ -32,7 +38,7 @@ LL |     fn map2<F>(self, f: F) -> Map2<F> {}
            found unit type `()`
 
 error[E0277]: the size for values of type `Self` cannot be known at compilation time
-  --> $DIR/issue-78720.rs:7:16
+  --> $DIR/issue-78720.rs:8:16
    |
 LL |     fn map2<F>(self, f: F) -> Map2<F> {}
    |                ^^^^ doesn't have a size known at compile-time
@@ -47,7 +53,7 @@ help: function arguments must have a statically known size, borrowed types alway
 LL |     fn map2<F>(&self, f: F) -> Map2<F> {}
    |                +
 
-error: aborting due to 4 previous errors
+error: aborting due to 5 previous errors
 
-Some errors have detailed explanations: E0277, E0308, E0412.
+Some errors have detailed explanations: E0277, E0282, E0308, E0412.
 For more information about an error, try `rustc --explain E0277`.
diff --git a/tests/ui/codegen/overflow-during-mono.rs b/tests/ui/codegen/overflow-during-mono.rs
index 83a8b6b3ef6..a9045840173 100644
--- a/tests/ui/codegen/overflow-during-mono.rs
+++ b/tests/ui/codegen/overflow-during-mono.rs
@@ -1,4 +1,4 @@
-//~ ERROR overflow evaluating the requirement `{closure@$DIR/overflow-during-mono.rs:13:41: 13:44}: Sized`
+//~ ERROR overflow evaluating the requirement `for<'a> {closure@$DIR/overflow-during-mono.rs:13:41: 13:44}: FnMut(&'a _)`
 //@ build-fail
 
 #![recursion_limit = "32"]
diff --git a/tests/ui/codegen/overflow-during-mono.stderr b/tests/ui/codegen/overflow-during-mono.stderr
index f7a3e2df3db..74d98fde285 100644
--- a/tests/ui/codegen/overflow-during-mono.stderr
+++ b/tests/ui/codegen/overflow-during-mono.stderr
@@ -1,4 +1,4 @@
-error[E0275]: overflow evaluating the requirement `{closure@$DIR/overflow-during-mono.rs:13:41: 13:44}: Sized`
+error[E0275]: overflow evaluating the requirement `for<'a> {closure@$DIR/overflow-during-mono.rs:13:41: 13:44}: FnMut(&'a _)`
    |
    = help: consider increasing the recursion limit by adding a `#![recursion_limit = "64"]` attribute to your crate (`overflow_during_mono`)
    = note: required for `Filter<std::array::IntoIter<i32, 11>, {closure@$DIR/overflow-during-mono.rs:13:41: 13:44}>` to implement `Iterator`