diff --git a/lib/mime/types.rb b/lib/mime/types.rb
index 026be34..05d7974 100644
--- a/lib/mime/types.rb
+++ b/lib/mime/types.rb
@@ -133,9 +133,7 @@ def [](type_id, complete: false, registered: false)
         @type_variants[MIME::Type.simplified(type_id)]
       end
 
-    prune_matches(matches, complete, registered).sort { |a, b|
-      a.priority_compare(b)
-    }
+    stable_sort(prune_matches(matches, complete, registered))
   end
 
   # Return the list of MIME::Types which belongs to the file based on its
@@ -151,11 +149,12 @@ def [](type_id, complete: false, registered: false)
   #   puts MIME::Types.type_for(%w(citydesk.xml citydesk.gif))
   #     => [application/xml, image/gif, text/xml]
   def type_for(filename)
-    Array(filename).flat_map { |fn|
-      @extension_index[fn.chomp.downcase[/\.?([^.]*?)\z/m, 1]]
-    }.compact.inject(Set.new, :+).sort { |a, b|
-      a.priority_compare(b)
-    }
+    results =
+      Array(filename).flat_map { |fn|
+        @extension_index[fn.chomp.downcase[/\.?([^.]*?)\z/m, 1]]
+      }.compact.inject(Set.new, :+)
+
+    stable_sort(results)
   end
   alias_method :of, :type_for
 
@@ -223,6 +222,12 @@ def match(pattern)
       k =~ pattern
     }.values.inject(Set.new, :+)
   end
+
+  def stable_sort(list)
+    list.lazy.each_with_index.sort { |(a, ai), (b, bi)|
+      a.priority_compare(b).nonzero? || ai <=> bi
+    }.map(&:first)
+  end
 end
 
 require "mime/types/cache"
diff --git a/test/test_mime_types.rb b/test/test_mime_types.rb
index a0812a8..e0e19c5 100644
--- a/test/test_mime_types.rb
+++ b/test/test_mime_types.rb
@@ -18,7 +18,8 @@ def mime_types
           "content-type" => "application/gzip",
           "extensions" => "gz",
           "registered" => true
-        )
+        ),
+        *MIME::Types.type_for("foo.webm")
     }
   end
 
@@ -38,8 +39,8 @@ def mime_types
     end
 
     it "is countable with an enumerator" do
-      assert_equal 6, mime_types.each.count
-      assert_equal 6, mime_types.lazy.count
+      assert_equal 8, mime_types.each.count
+      assert_equal 8, mime_types.lazy.count
     end
   end
 
@@ -163,11 +164,15 @@ def mime_types
     it "handles newline characters correctly" do
       assert_includes mime_types.type_for("test.pdf\n.txt"), "text/plain"
     end
+
+    it "returns a stable order for types with equal priority" do
+      assert_equal %w[audio/webm video/webm], mime_types.type_for("foo.webm")
+    end
   end
 
   describe "#count" do
     it "can count the number of types inside" do
-      assert_equal 6, mime_types.count
+      assert_equal 8, mime_types.count
     end
   end
 end
diff --git a/test/test_mime_types_class.rb b/test/test_mime_types_class.rb
index 08e9556..f219cb5 100644
--- a/test/test_mime_types_class.rb
+++ b/test/test_mime_types_class.rb
@@ -105,6 +105,10 @@ def setup
       assert_includes MIME::Types.type_for("test.pdf\n.txt"), "text/plain"
       assert_includes MIME::Types.type_for("test.txt\n.pdf"), "application/pdf"
     end
+
+    it "returns a stable order for types with equal priority" do
+      assert_equal %w[audio/webm video/webm], MIME::Types.type_for("foo.webm")
+    end
   end
 
   describe ".count" do