diff --git a/core/symbol.rbs b/core/symbol.rbs
index fafd9c578..d283858cd 100644
--- a/core/symbol.rbs
+++ b/core/symbol.rbs
@@ -151,7 +151,7 @@ class Symbol
   # Related: String#<=>.
   #
   def <=>: (Symbol object) -> (-1 | 0 | 1)
-         | (untyped) -> nil
+         | (untyped) -> (-1 | 0 | 1)?
 
   # <!--
   #   rdoc-file=string.c
@@ -236,8 +236,7 @@ class Symbol
   #
   # Related: Symbol#casecmp?, String#casecmp.
   #
-  def casecmp: (Symbol object) -> (-1 | 0 | 1)?
-             | (untyped) -> nil
+  def casecmp: (untyped object) -> (-1 | 0 | 1)?
 
   # <!--
   #   rdoc-file=string.c
@@ -270,8 +269,7 @@ class Symbol
   #
   # Related: Symbol#casecmp, String#casecmp?.
   #
-  def casecmp?: (Symbol object) -> bool?
-              | (untyped) -> nil
+  def casecmp?: (untyped object) -> bool?
 
   # <!--
   #   rdoc-file=string.c
diff --git a/test/stdlib/Symbol_test.rb b/test/stdlib/Symbol_test.rb
index 4603dab1c..c27ac8904 100644
--- a/test/stdlib/Symbol_test.rb
+++ b/test/stdlib/Symbol_test.rb
@@ -22,10 +22,8 @@ def test_op_cmp
                        :s, :<=>, other
     end
 
-    with_untyped do |untyped|
-      next if Symbol === untyped
-
-      assert_send_type '(untyped) -> nil',
+    with_untyped.and :sym do |untyped|
+      assert_send_type '(untyped) -> Integer?',
                        :a, :<=>, untyped
     end
   end
@@ -127,10 +125,8 @@ def test_casecmp
     assert_send_type '(Symbol) -> nil',
                      "\u{e4 f6 fc}".encode('ISO-8859-1').to_sym, :casecmp, :"\u{c4 d6 dc}"
 
-    with_untyped do |other|
-      next if Symbol === other
-
-      assert_send_type '(untyped) -> nil',
+    with_untyped.and :sym do |other|
+      assert_send_type '(untyped) -> (-1 | 0 | 1)?',
                        :a, :casecmp, other
     end
   end
@@ -145,10 +141,8 @@ def test_casecmp?
     assert_send_type '(Symbol) -> nil',
                      '\u{e4 f6 fc}'.encode('ISO-8859-1').to_sym, :casecmp?, :'\u{c4 d6 dc}'
 
-    with_untyped do |other|
-      next if Symbol === other
-
-      assert_send_type '(untyped) -> nil',
+    with_untyped.and :sym do |other|
+      assert_send_type '(untyped) -> bool?',
                        :a, :casecmp?, other
     end
   end