diff --git a/core/class.rbs b/core/class.rbs
index abfdc2164..bb27a1cc8 100644
--- a/core/class.rbs
+++ b/core/class.rbs
@@ -82,7 +82,7 @@ class Class < Module
   # Assign the class to a constant (name starting uppercase) if you want to treat
   # it like a regular class.
   #
-  def initialize: (?Class superclass) ?{ (Class newclass) -> void } -> void
+  def initialize: (?Class superclass) ?{ (Class newclass) [self: Class] -> void } -> void
 
   # <!--
   #   rdoc-file=object.c
@@ -106,6 +106,8 @@ class Class < Module
   #
   def allocate: () -> untyped
 
+  def self.allocate: () -> untyped
+
   # <!--
   #   rdoc-file=object.c
   #   - attached_object -> object
@@ -149,7 +151,7 @@ class Class < Module
   #     New subclass: Bar
   #     New subclass: Baz
   #
-  def inherited: (Class arg0) -> untyped
+  private def inherited: (Class subclass) -> void
 
   # <!--
   #   rdoc-file=object.c
@@ -159,7 +161,7 @@ class Class < Module
   # object's #initialize method, passing it *args*.  This is the method that ends
   # up getting called whenever an object is constructed using `.new`.
   #
-  def new: () -> untyped
+  def new: (*untyped, **untyped) ?{ (?) -> untyped } -> untyped
 
   # <!--
   #   rdoc-file=object.c
diff --git a/test/stdlib/Class_test.rb b/test/stdlib/Class_test.rb
index 6a04c29bc..ad36130a2 100644
--- a/test/stdlib/Class_test.rb
+++ b/test/stdlib/Class_test.rb
@@ -1,32 +1,73 @@
 require_relative "test_helper"
 
-class ClassTest < StdlibTest
-  target Class
+class ClassSingletonTest < Test::Unit::TestCase
+  include TestHelper
 
-  def test_singleton_new
-    Class.new()
-    Class.new(Integer)
-    Class.new { }
+  testing "singleton(::Class)"
+
+  def test_allocate
+    assert_send_type "() -> untyped",
+                     Class, :new
   end
+end
+
+class ClassInstanceTest < Test::Unit::TestCase
+  include TestHelper
+
+  testing "::Class"
+
+  Subclass = Class.new
 
   def test_allocate
-    Class.new.allocate
+    assert_send_type "() -> untyped",
+                     Subclass, :new
   end
 
-  def test_instance_new
-    Class.new.new
+  def test_new
+    assert_send_type  '() -> untyped',
+                      Subclass, :new
+
+    big_init = Class.new do
+      def initialize(*a, **k, &b) = nil
+    end
+
+    assert_send_type  '(*untyped, **untyped) { (?) -> untyped } -> untyped',
+                      big_init, :new, 1, 2, a: 3, 'b' => 4 do |x, y, &z| 3 end
   end
 
-  def test_super_class
-    Class.new.superclass
-    BasicObject.superclass
+  def test_initialize
+    assert_send_type "() -> void",
+                     Class.allocate, :initialize
+
+    assert_send_type "() { (Class) [self: Class] -> void } -> void",
+                     Class.allocate, :initialize do end
+
+    assert_send_type "(Class) -> void",
+                     Class.allocate, :initialize, String
+
+    assert_send_type "(Class) { (Class) [self: Class] -> void } -> void",
+                     Class.allocate, :initialize, String do end
+  end
+
+  def test_superclass
+    assert_send_type "() -> Class",
+                     String, :superclass
+    assert_send_type "() -> nil",
+                     BasicObject, :superclass
   end
 
   def test_subclasses
-    Class.new.subclasses
+    assert_send_type "() -> Array[Class]",
+                     Module, :subclasses
   end
 
   def test_attached_object
-    Class.new.singleton_class.attached_object
+    assert_send_type "() -> untyped",
+                     Subclass.new.singleton_class, :attached_object
+  end
+
+  def test_inherited
+    assert_send_type "(Class) -> void",
+                     Subclass, :inherited, String
   end
 end