diff --git a/src/librustc/traits/coherence.rs b/src/librustc/traits/coherence.rs
index 855da0367de06..c6a12279539c9 100644
--- a/src/librustc/traits/coherence.rs
+++ b/src/librustc/traits/coherence.rs
@@ -11,10 +11,11 @@ use crate::traits::SkipLeakCheck;
 use crate::traits::{self, Normalized, Obligation, ObligationCause, SelectionContext};
 use crate::ty::fold::TypeFoldable;
 use crate::ty::subst::Subst;
-use crate::ty::{self, Ty, TyCtxt};
+use crate::ty::{self, fast_reject, Ty, TyCtxt};
 use rustc_hir::def_id::{DefId, LOCAL_CRATE};
 use rustc_span::symbol::sym;
 use rustc_span::DUMMY_SP;
+use std::iter;
 
 /// Whether we do the orphan check relative to this crate or
 /// to some remote crate.
@@ -70,6 +71,37 @@ where
         impl1_def_id, impl2_def_id, intercrate_mode
     );
 
+    // 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.
+    let impl1_self = tcx.type_of(impl1_def_id);
+    let impl2_self = tcx.type_of(impl2_def_id);
+    let impl1_ref = tcx.impl_trait_ref(impl1_def_id);
+    let impl2_ref = tcx.impl_trait_ref(impl2_def_id);
+
+    // Check if any of the input types definitely mismatch.
+    if impl1_ref
+        .iter()
+        .flat_map(|tref| tref.input_types())
+        .zip(impl2_ref.iter().flat_map(|tref| tref.input_types()))
+        .chain(iter::once((impl1_self, impl2_self)))
+        .any(|(ty1, ty2)| {
+            let ty1 = fast_reject::simplify_type(tcx, ty1, false);
+            let ty2 = fast_reject::simplify_type(tcx, ty2, false);
+            if let (Some(ty1), Some(ty2)) = (ty1, ty2) {
+                // Simplified successfully
+                ty1 != ty2
+            } else {
+                // Types might unify
+                false
+            }
+        })
+    {
+        // Some types involved are definitely different, so the impls couldn't possibly overlap.
+        debug!("overlapping_impls: fast_reject early-exit");
+        return no_overlap();
+    }
+
     let overlaps = tcx.infer_ctxt().enter(|infcx| {
         let selcx = &mut SelectionContext::intercrate(&infcx, intercrate_mode);
         overlap(selcx, skip_leak_check, impl1_def_id, impl2_def_id).is_some()