diff --git a/src/librustc/traits/specialize/mod.rs b/src/librustc/traits/specialize/mod.rs
index f0389bb037ac5..8a84fca143809 100644
--- a/src/librustc/traits/specialize/mod.rs
+++ b/src/librustc/traits/specialize/mod.rs
@@ -366,8 +366,13 @@ pub(super) fn specialization_graph_provider(
                     }
                 }
 
-                for cause in &overlap.intercrate_ambiguity_causes {
-                    cause.add_intercrate_ambiguity_hint(&mut err);
+                let access_levels = tcx.privacy_access_levels(impl_def_id.krate);
+                if let Some(id) = tcx.hir().as_local_hir_id(impl_def_id) {
+                    if access_levels.is_exported(id) || access_levels.is_public(id) {
+                        for cause in &overlap.intercrate_ambiguity_causes {
+                            cause.add_intercrate_ambiguity_hint(&mut err);
+                        }
+                    }
                 }
 
                 if overlap.involves_placeholder {
diff --git a/src/test/ui/coherence/coherence-overlap-upstream.old.stderr b/src/test/ui/coherence/coherence-overlap-upstream.old.stderr
index 6c3484c2d8c4d..dea948ff8abbb 100644
--- a/src/test/ui/coherence/coherence-overlap-upstream.old.stderr
+++ b/src/test/ui/coherence/coherence-overlap-upstream.old.stderr
@@ -5,8 +5,6 @@ LL | impl<T> Foo for T where T: Remote {}
    | --------------------------------- first implementation here
 LL | impl Foo for i16 {}
    | ^^^^^^^^^^^^^^^^ conflicting implementation for `i16`
-   |
-   = note: upstream crates may add new impl of trait `coherence_lib::Remote` for type `i16` in future versions
 
 error: aborting due to previous error
 
diff --git a/src/test/ui/coherence/coherence-overlap-upstream.re.stderr b/src/test/ui/coherence/coherence-overlap-upstream.re.stderr
index 6c3484c2d8c4d..dea948ff8abbb 100644
--- a/src/test/ui/coherence/coherence-overlap-upstream.re.stderr
+++ b/src/test/ui/coherence/coherence-overlap-upstream.re.stderr
@@ -5,8 +5,6 @@ LL | impl<T> Foo for T where T: Remote {}
    | --------------------------------- first implementation here
 LL | impl Foo for i16 {}
    | ^^^^^^^^^^^^^^^^ conflicting implementation for `i16`
-   |
-   = note: upstream crates may add new impl of trait `coherence_lib::Remote` for type `i16` in future versions
 
 error: aborting due to previous error
 
diff --git a/src/test/ui/coherence/coherence_copy_like_err_fundamental_struct_tuple.old.stderr b/src/test/ui/coherence/coherence_copy_like_err_fundamental_struct_tuple.old.stderr
index 12c7a1f977c3f..0ec4f0bb8e74d 100644
--- a/src/test/ui/coherence/coherence_copy_like_err_fundamental_struct_tuple.old.stderr
+++ b/src/test/ui/coherence/coherence_copy_like_err_fundamental_struct_tuple.old.stderr
@@ -6,8 +6,6 @@ LL | impl<T: lib::MyCopy> MyTrait for T { }
 ...
 LL | impl MyTrait for lib::MyFundamentalStruct<(MyType,)> { }
    | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ conflicting implementation for `lib::MyFundamentalStruct<(MyType,)>`
-   |
-   = note: upstream crates may add new impl of trait `lib::MyCopy` for type `lib::MyFundamentalStruct<(MyType,)>` in future versions
 
 error: aborting due to previous error
 
diff --git a/src/test/ui/coherence/coherence_copy_like_err_fundamental_struct_tuple.re.stderr b/src/test/ui/coherence/coherence_copy_like_err_fundamental_struct_tuple.re.stderr
index 12c7a1f977c3f..0ec4f0bb8e74d 100644
--- a/src/test/ui/coherence/coherence_copy_like_err_fundamental_struct_tuple.re.stderr
+++ b/src/test/ui/coherence/coherence_copy_like_err_fundamental_struct_tuple.re.stderr
@@ -6,8 +6,6 @@ LL | impl<T: lib::MyCopy> MyTrait for T { }
 ...
 LL | impl MyTrait for lib::MyFundamentalStruct<(MyType,)> { }
    | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ conflicting implementation for `lib::MyFundamentalStruct<(MyType,)>`
-   |
-   = note: upstream crates may add new impl of trait `lib::MyCopy` for type `lib::MyFundamentalStruct<(MyType,)>` in future versions
 
 error: aborting due to previous error
 
diff --git a/src/test/ui/coherence/coherence_copy_like_err_struct.old.stderr b/src/test/ui/coherence/coherence_copy_like_err_struct.old.stderr
index 1b6c62e9bf3a8..e5862fdda7c58 100644
--- a/src/test/ui/coherence/coherence_copy_like_err_struct.old.stderr
+++ b/src/test/ui/coherence/coherence_copy_like_err_struct.old.stderr
@@ -6,8 +6,6 @@ LL | impl<T: lib::MyCopy> MyTrait for T { }
 ...
 LL | impl MyTrait for lib::MyStruct<MyType> { }
    | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ conflicting implementation for `lib::MyStruct<MyType>`
-   |
-   = note: upstream crates may add new impl of trait `lib::MyCopy` for type `lib::MyStruct<MyType>` in future versions
 
 error: aborting due to previous error
 
diff --git a/src/test/ui/coherence/coherence_copy_like_err_struct.re.stderr b/src/test/ui/coherence/coherence_copy_like_err_struct.re.stderr
index 1b6c62e9bf3a8..e5862fdda7c58 100644
--- a/src/test/ui/coherence/coherence_copy_like_err_struct.re.stderr
+++ b/src/test/ui/coherence/coherence_copy_like_err_struct.re.stderr
@@ -6,8 +6,6 @@ LL | impl<T: lib::MyCopy> MyTrait for T { }
 ...
 LL | impl MyTrait for lib::MyStruct<MyType> { }
    | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ conflicting implementation for `lib::MyStruct<MyType>`
-   |
-   = note: upstream crates may add new impl of trait `lib::MyCopy` for type `lib::MyStruct<MyType>` in future versions
 
 error: aborting due to previous error
 
diff --git a/src/test/ui/coherence/coherence_copy_like_err_tuple.old.stderr b/src/test/ui/coherence/coherence_copy_like_err_tuple.old.stderr
index 11bd788c76153..a3c4ef8e105a2 100644
--- a/src/test/ui/coherence/coherence_copy_like_err_tuple.old.stderr
+++ b/src/test/ui/coherence/coherence_copy_like_err_tuple.old.stderr
@@ -6,8 +6,6 @@ LL | impl<T: lib::MyCopy> MyTrait for T { }
 ...
 LL | impl MyTrait for (MyType,) { }
    | ^^^^^^^^^^^^^^^^^^^^^^^^^^ conflicting implementation for `(MyType,)`
-   |
-   = note: upstream crates may add new impl of trait `lib::MyCopy` for type `(MyType,)` in future versions
 
 error: aborting due to previous error
 
diff --git a/src/test/ui/coherence/coherence_copy_like_err_tuple.re.stderr b/src/test/ui/coherence/coherence_copy_like_err_tuple.re.stderr
index 11bd788c76153..a3c4ef8e105a2 100644
--- a/src/test/ui/coherence/coherence_copy_like_err_tuple.re.stderr
+++ b/src/test/ui/coherence/coherence_copy_like_err_tuple.re.stderr
@@ -6,8 +6,6 @@ LL | impl<T: lib::MyCopy> MyTrait for T { }
 ...
 LL | impl MyTrait for (MyType,) { }
    | ^^^^^^^^^^^^^^^^^^^^^^^^^^ conflicting implementation for `(MyType,)`
-   |
-   = note: upstream crates may add new impl of trait `lib::MyCopy` for type `(MyType,)` in future versions
 
 error: aborting due to previous error
 
diff --git a/src/test/ui/issues/issue-48728.stderr b/src/test/ui/issues/issue-48728.stderr
index 99a9bf9903e25..777e1fc9c27ea 100644
--- a/src/test/ui/issues/issue-48728.stderr
+++ b/src/test/ui/issues/issue-48728.stderr
@@ -6,8 +6,6 @@ LL | #[derive(Clone)]
 ...
 LL | impl<T: Clone + ?Sized> Clone for Node<[T]> {
    | ------------------------------------------- first implementation here
-   |
-   = note: upstream crates may add new impl of trait `std::clone::Clone` for type `[_]` in future versions
 
 error: aborting due to previous error
 
diff --git a/src/test/ui/specialization/issue-52050.stderr b/src/test/ui/specialization/issue-52050.stderr
index dcb34f3ad4836..583c580d341ba 100644
--- a/src/test/ui/specialization/issue-52050.stderr
+++ b/src/test/ui/specialization/issue-52050.stderr
@@ -10,8 +10,6 @@ LL | | }
 LL | 
 LL |   impl IntoPyDictPointer for ()
    |   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ conflicting implementation for `()`
-   |
-   = note: upstream crates may add new impl of trait `std::iter::Iterator` for type `()` in future versions
 
 error: aborting due to previous error