Index: llvm/lib/Transforms/IPO/Attributor.cpp
===================================================================
--- llvm/lib/Transforms/IPO/Attributor.cpp
+++ llvm/lib/Transforms/IPO/Attributor.cpp
@@ -2971,6 +2971,16 @@
     return TrackUse;
   }
 
+  /// See AbstractAttribute::manifest(...).
+  ChangeStatus manifest(Attributor &A) override {
+    ChangeStatus Change = AADereferenceable::manifest(A);
+    if (isAssumedNonNull() && hasAttr(Attribute::DereferenceableOrNull)) {
+      removeAttrs({Attribute::DereferenceableOrNull});
+      return ChangeStatus::CHANGED;
+    }
+    return Change;
+  }
+
   void getDeducedAttributes(LLVMContext &Ctx,
                             SmallVectorImpl<Attribute> &Attrs) const override {
     // TODO: Add *_globally support
Index: llvm/test/Transforms/FunctionAttrs/dereferenceable.ll
===================================================================
--- llvm/test/Transforms/FunctionAttrs/dereferenceable.ll
+++ llvm/test/Transforms/FunctionAttrs/dereferenceable.ll
@@ -30,8 +30,7 @@
 }
 
 define i32* @test3_2(i32* dereferenceable_or_null(32) %0) local_unnamed_addr {
-; FIXME: We should not have both deref(x) and deref_or_null(y) with x >= y.
-; ATTRIBUTOR: define nonnull dereferenceable(16) i32* @test3_2(i32* nofree nonnull readnone dereferenceable(32) dereferenceable_or_null(32) "no-capture-maybe-returned" %0)
+; ATTRIBUTOR: define nonnull dereferenceable(16) i32* @test3_2(i32* nofree nonnull readnone dereferenceable(32) "no-capture-maybe-returned" %0)
   %ret = getelementptr inbounds i32, i32* %0, i64 4
   ret i32* %ret
 }
@@ -202,3 +201,9 @@
   store i32 1, i32* %q
   ret i32* %q
 }
+
+define void @deref_or_null_and_nonnull(i32* dereferenceable_or_null(100) %0) {
+; ATTRIBUTOR: define void @deref_or_null_and_nonnull(i32* nocapture nofree nonnull writeonly dereferenceable(100) %0)
+  store i32 1, i32* %0
+  ret void
+}