diff --git a/src/test/compile-fail/feature-gate-overlapping_marker_traits.rs b/src/test/compile-fail/feature-gate-overlapping_marker_traits.rs
index bf2b06dd8ba..d2aa4e59b5b 100644
--- a/src/test/compile-fail/feature-gate-overlapping_marker_traits.rs
+++ b/src/test/compile-fail/feature-gate-overlapping_marker_traits.rs
@@ -8,10 +8,12 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
+use std::fmt::{Debug, Display};
+
 trait MyMarker {}
 
-impl<T> MyMarker for T {}
-impl<T> MyMarker for Vec<T> {}
+impl<T: Display> MyMarker for T {}
+impl<T: Debug> MyMarker for T {}
 //~^ ERROR E0119
 
 fn main() {}
diff --git a/src/test/compile-fail/overlap-marker-trait.rs b/src/test/compile-fail/overlap-marker-trait.rs
new file mode 100644
index 00000000000..a649ae25f34
--- /dev/null
+++ b/src/test/compile-fail/overlap-marker-trait.rs
@@ -0,0 +1,41 @@
+// Copyright 2017 The Rust Project Developers. See the COPYRIGHT
+// file at the top-level directory of this distribution and at
+// http://rust-lang.org/COPYRIGHT.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+// Test for RFC 1268: we allow overlapping impls of marker traits,
+// that is, traits without items. In this case, a type `T` is
+// `MyMarker` if it is either `Debug` or `Display`. This test just
+// checks that we don't consider **all** types to be `MyMarker`.  See
+// also the companion test in
+// `run-pass/overlap-permitted-for-marker-traits.rs`.
+
+#![feature(overlapping_marker_traits)]
+#![feature(optin_builtin_traits)]
+
+use std::fmt::{Debug, Display};
+
+trait Marker {}
+
+impl<T: Debug> Marker for T {}
+impl<T: Display> Marker for T {}
+
+fn is_marker<T: Marker>() { }
+
+struct NotDebugOrDisplay;
+
+fn main() {
+    // Debug && Display:
+    is_marker::<i32>();
+
+    // Debug && !Display:
+    is_marker::<Vec<i32>>();
+
+    // !Debug && !Display
+    is_marker::<NotDebugOrDisplay>(); //~ ERROR
+}
diff --git a/src/test/run-pass/overlap-permitted-for-marker-traits-neg.rs b/src/test/run-pass/overlap-permitted-for-marker-traits-neg.rs
new file mode 100644
index 00000000000..740d5d22ab5
--- /dev/null
+++ b/src/test/run-pass/overlap-permitted-for-marker-traits-neg.rs
@@ -0,0 +1,20 @@
+// Copyright 2017 The Rust Project Developers. See the COPYRIGHT
+// file at the top-level directory of this distribution and at
+// http://rust-lang.org/COPYRIGHT.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+#![feature(overlapping_marker_traits)]
+#![feature(optin_builtin_traits)]
+
+// Overlapping negative impls for `MyStruct` are permitted:
+struct MyStruct;
+impl !Send for MyStruct {}
+impl !Send for MyStruct {}
+
+fn main() {
+}
diff --git a/src/test/run-pass/overlap-permitted-for-marker-traits.rs b/src/test/run-pass/overlap-permitted-for-marker-traits.rs
index 45085c093fc..11a46299d8c 100644
--- a/src/test/run-pass/overlap-permitted-for-marker-traits.rs
+++ b/src/test/run-pass/overlap-permitted-for-marker-traits.rs
@@ -8,24 +8,29 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
+// Tests for RFC 1268: we allow overlapping impls of marker traits,
+// that is, traits without items. In this case, a type `T` is
+// `MyMarker` if it is either `Debug` or `Display`.
+
 #![feature(overlapping_marker_traits)]
 #![feature(optin_builtin_traits)]
 
+use std::fmt::{Debug, Display};
+
 trait MyMarker {}
 
-impl<T: Copy> MyMarker for T {}
-impl<T: Eq> MyMarker for T {}
-
-struct MyStruct;
-impl !Send for MyStruct {}
-impl !Send for MyStruct {}
+impl<T: Debug> MyMarker for T {}
+impl<T: Display> MyMarker for T {}
 
 fn foo<T: MyMarker>(t: T) -> T {
     t
 }
 
 fn main() {
+    // Debug && Display:
     assert_eq!(1, foo(1));
     assert_eq!(2.0, foo(2.0));
+
+    // Debug && !Display:
     assert_eq!(vec![1], foo(vec![1]));
 }