diff --git a/src/librustc/traits/query/type_op/prove_predicate.rs b/src/librustc/traits/query/type_op/prove_predicate.rs
index 33dc3210f0881..e1b3b3c436dab 100644
--- a/src/librustc/traits/query/type_op/prove_predicate.rs
+++ b/src/librustc/traits/query/type_op/prove_predicate.rs
@@ -27,9 +27,23 @@ impl<'gcx: 'tcx, 'tcx> super::QueryTypeOp<'gcx, 'tcx> for ProvePredicate<'tcx> {
     type QueryResult = ();
 
     fn try_fast_path(
-        _tcx: TyCtxt<'_, 'gcx, 'tcx>,
-        _key: &ParamEnvAnd<'tcx, Self>,
+        tcx: TyCtxt<'_, 'gcx, 'tcx>,
+        key: &ParamEnvAnd<'tcx, Self>,
     ) -> Option<Self::QueryResult> {
+        // 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 Predicate::Trait(trait_ref) = key.value.predicate {
+            if let Some(sized_def_id) = tcx.lang_items().sized_trait() {
+                if trait_ref.def_id() == sized_def_id {
+                    if trait_ref.skip_binder().self_ty().is_trivially_sized(tcx) {
+                        return Some(());
+                    }
+                }
+            }
+        }
+
         None
     }
 
diff --git a/src/librustc/ty/sty.rs b/src/librustc/ty/sty.rs
index 96b4edce86b30..6adafb8602c9a 100644
--- a/src/librustc/ty/sty.rs
+++ b/src/librustc/ty/sty.rs
@@ -1852,6 +1852,41 @@ impl<'a, 'gcx, 'tcx> TyS<'tcx> {
             _ => bug!("cannot convert type `{:?}` to a closure kind", self),
         }
     }
+
+    /// 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.
+    pub fn is_trivially_sized(&self, tcx: TyCtxt<'_, '_, 'tcx>) -> bool {
+        match self.sty {
+            ty::TyInfer(ty::IntVar(_)) | ty::TyInfer(ty::FloatVar(_)) |
+            ty::TyUint(_) | ty::TyInt(_) | ty::TyBool | ty::TyFloat(_) |
+            ty::TyFnDef(..) | ty::TyFnPtr(_) | ty::TyRawPtr(..) |
+            ty::TyChar | ty::TyRef(..) | ty::TyGenerator(..) |
+            ty::TyGeneratorWitness(..) | ty::TyArray(..) | ty::TyClosure(..) |
+            ty::TyNever | ty::TyError =>
+                true,
+
+            ty::TyStr | ty::TySlice(_) | ty::TyDynamic(..) | ty::TyForeign(..) =>
+                false,
+
+            ty::TyTuple(tys) =>
+                tys.iter().all(|ty| ty.is_trivially_sized(tcx)),
+
+            ty::TyAdt(def, _substs) =>
+                def.sized_constraint(tcx).is_empty(),
+
+            ty::TyProjection(_) | ty::TyParam(_) | ty::TyAnon(..) => false,
+
+            ty::TyInfer(ty::TyVar(_)) => false,
+
+            ty::TyInfer(ty::CanonicalTy(_)) |
+            ty::TyInfer(ty::FreshTy(_)) |
+            ty::TyInfer(ty::FreshIntTy(_)) |
+            ty::TyInfer(ty::FreshFloatTy(_)) =>
+                bug!("is_trivially_sized applied to unexpected type: {:?}", self),
+        }
+    }
 }
 
 /// Typed constant value.