diff --git a/lib/repl_type_completor/types.rb b/lib/repl_type_completor/types.rb
index c002284..9984c24 100644
--- a/lib/repl_type_completor/types.rb
+++ b/lib/repl_type_completor/types.rb
@@ -162,7 +162,7 @@ def initialize(module_or_class)
       end
       def transform() = yield(self)
       def methods() = @module_or_class.methods
-      def all_methods() = methods | Kernel.methods
+      def all_methods() = methods | @module_or_class.private_methods
       def constants() = @module_or_class.constants
       def types() = [self]
       def nillable?() = false
diff --git a/test/repl_type_completor/test_types.rb b/test/repl_type_completor/test_types.rb
index 642b2dd..fadf14f 100644
--- a/test/repl_type_completor/test_types.rb
+++ b/test/repl_type_completor/test_types.rb
@@ -66,16 +66,30 @@ def foobar; end
         private def foobaz; end
       end
       String.define_method(:foobarbaz) {}
-      targets = [:foobar, :foobaz, :foobarbaz]
+      targets = [:foobar, :foobaz, :foobarbaz, :rand]
       type = ReplTypeCompletor::Types.type_from_object s
       assert_equal [:foobar, :foobarbaz], targets & type.methods
-      assert_equal [:foobar, :foobaz, :foobarbaz], targets & type.all_methods
+      assert_equal [:foobar, :foobaz, :foobarbaz, :rand], targets & type.all_methods
       assert_equal [:foobarbaz], targets & ReplTypeCompletor::Types::STRING.methods
-      assert_equal [:foobarbaz], targets & ReplTypeCompletor::Types::STRING.all_methods
+      assert_equal [:foobarbaz, :rand], targets & ReplTypeCompletor::Types::STRING.all_methods
     ensure
       String.remove_method :foobarbaz
     end
 
+    def test_singleton_type_methods
+      m = Module.new do
+        class << self
+          def foobar; end
+          private def foobaz; end
+        end
+      end
+      type = ReplTypeCompletor::Types::SingletonType.new(m)
+      assert_include type.methods, :foobar
+      assert_not_include type.methods, :foobaz
+      assert_include type.all_methods, :foobaz
+      assert_include type.all_methods, :rand
+    end
+
     def test_basic_object_methods
       bo = BasicObject.new
       def bo.foobar; end