diff --git a/clang/lib/Lex/ModuleMap.cpp b/clang/lib/Lex/ModuleMap.cpp
index 637a08fe4dcdb..fc0a0c1cfc873 100644
--- a/clang/lib/Lex/ModuleMap.cpp
+++ b/clang/lib/Lex/ModuleMap.cpp
@@ -572,16 +572,16 @@ static bool isBetterKnownHeader(const ModuleMap::KnownHeader &New,
   if (New.getModule()->isAvailable() && !Old.getModule()->isAvailable())
     return true;
 
-  // Prefer a public header over a private header.
-  if ((New.getRole() & ModuleMap::PrivateHeader) !=
-      (Old.getRole() & ModuleMap::PrivateHeader))
-    return !(New.getRole() & ModuleMap::PrivateHeader);
-
   // Prefer a non-textual header over a textual header.
   if ((New.getRole() & ModuleMap::TextualHeader) !=
       (Old.getRole() & ModuleMap::TextualHeader))
     return !(New.getRole() & ModuleMap::TextualHeader);
 
+  // Prefer a public header over a private header.
+  if ((New.getRole() & ModuleMap::PrivateHeader) !=
+      (Old.getRole() & ModuleMap::PrivateHeader))
+    return !(New.getRole() & ModuleMap::PrivateHeader);
+
   // Prefer a non-excluded header over an excluded header.
   if ((New.getRole() == ModuleMap::ExcludedHeader) !=
       (Old.getRole() == ModuleMap::ExcludedHeader))
diff --git a/clang/test/Modules/multiple-modules-per-header-embed-all-files.cpp b/clang/test/Modules/multiple-modules-per-header-embed-all-files.cpp
new file mode 100644
index 0000000000000..19f1db1689667
--- /dev/null
+++ b/clang/test/Modules/multiple-modules-per-header-embed-all-files.cpp
@@ -0,0 +1,60 @@
+// RUN: rm -rf %t
+// RUN: split-file %s %t
+//
+// First, build a module with a header.
+//
+// RUN: %clang_cc1 -fmodules -fmodule-map-file=%t/modules1.map -fmodule-name=a -emit-module -xc++ -fmodules-embed-all-files -o %t/a.pcm %t/modules1.map
+// RUN: %clang_cc1 -fmodules -fmodule-map-file=%t/modules1.map -fmodule-map-file=%t/modules2.map -fmodule-name=b -emit-module \
+// RUN:   -fmodule-file=%t/a.pcm -xc++ -fmodules-embed-all-files -o %t/b.pcm %t/modules2.map
+// 
+// Remove the header and check we can still build the code that finds it in a PCM.
+//
+// RUN: rm %t/foo.h
+// RUN: %clang_cc1 -fmodules -fmodule-map-file=%t/modules2.map -fmodule-file=%t/b.pcm -fsyntax-only %t/use.cpp
+
+//--- modules1.map
+module a {
+  module foo {
+    header "foo.h"
+    export *
+  }
+  export *
+}
+
+//--- modules2.map
+module all_textual {
+  module foo {
+    textual header "foo.h"
+    export *
+  }
+  module wrap_foo {
+    textual header "wrap_foo.h"
+    export *
+  }
+  export *
+}
+
+module b {
+  module wrap_foo {
+    private header "wrap_foo.h"
+    export *
+  }
+  export *
+}
+
+
+//--- foo.h
+#ifndef FOO_H
+#define FOO_H
+void foo();
+#endif
+
+//--- wrap_foo.h
+#include "foo.h"
+
+//--- use.cpp
+#include "wrap_foo.h"
+
+void test() {
+  foo();
+}