diff --git a/core/module.rbs b/core/module.rbs
index 0f19cf9a3..d3cf2c217 100644
--- a/core/module.rbs
+++ b/core/module.rbs
@@ -726,8 +726,8 @@ class Module < Object
   #     I'm Dino!
   #     #<B:0x401b39e8>
   #
-  def define_method: (id arg0, ?Proc | Method | UnboundMethod arg1) -> Symbol
-                   | (id arg0) { () -> untyped } -> Symbol
+  def define_method: (id symbol, Proc | Method | UnboundMethod method) -> Symbol
+                   | (id symbol) { () -> untyped } -> Symbol
 
   # <!--
   #   rdoc-file=object.c
diff --git a/core/object.rbs b/core/object.rbs
index ce13b8405..d6e1614ad 100644
--- a/core/object.rbs
+++ b/core/object.rbs
@@ -205,7 +205,7 @@ class Object < BasicObject
   #     chris.define_singleton_method(:greet) {|greeting| "#{greeting}, I'm Chris!" }
   #     chris.greet("Hi") #=> "Hi, I'm Chris!"
   #
-  def define_singleton_method: (name, Method | UnboundMethod) -> Symbol
+  def define_singleton_method: (name, Method | UnboundMethod | Proc method) -> Symbol
                              | (name) { (*untyped) -> untyped } -> Symbol
 
   # <!--
diff --git a/test/stdlib/Object_test.rb b/test/stdlib/Object_test.rb
index c9fec85d4..4877d7e7d 100644
--- a/test/stdlib/Object_test.rb
+++ b/test/stdlib/Object_test.rb
@@ -206,3 +206,41 @@ def test_to_s
     Object.new.to_s
   end
 end
+
+
+class ObjectInstanceTest < Test::Unit::TestCase
+  include TypeAssertions
+
+  testing "::Object"
+
+  def test_define_singleton_method
+    obj = Object.new
+
+    assert_send_type(
+      "(::Symbol) { () -> void } -> Symbol",
+      obj, :define_singleton_method,
+      :foo
+    ) do end
+
+    assert_send_type(
+      "(::Symbol, ::Proc) -> Symbol",
+      obj, :define_singleton_method,
+      :bar,
+      -> {}
+    )
+
+    assert_send_type(
+      "(::Symbol, ::Method) -> Symbol",
+      obj, :define_singleton_method,
+      :bar,
+      obj.method(:to_s)
+    )
+
+    assert_send_type(
+      "(::Symbol, ::UnboundMethod) -> Symbol",
+      obj, :define_singleton_method,
+      :bar,
+      Object.instance_method(:to_s)
+    )
+  end
+end