diff --git a/rules/__tests__/prefer_to_be_undefined.test.js b/rules/__tests__/prefer_to_be_undefined.test.js
index 369f13c27..e9f9fbea6 100644
--- a/rules/__tests__/prefer_to_be_undefined.test.js
+++ b/rules/__tests__/prefer_to_be_undefined.test.js
@@ -9,6 +9,8 @@ ruleTester.run('prefer_to_be_undefined', rules['prefer-to-be-undefined'], {
   valid: [
     'expect(undefined).toBeUndefined();',
     'expect(true).not.toBeUndefined();',
+    'expect({}).toEqual({});',
+    'expect(null).toEqual(null);',
   ],
 
   invalid: [
diff --git a/rules/util.js b/rules/util.js
index 9d049e021..492e883b1 100644
--- a/rules/util.js
+++ b/rules/util.js
@@ -27,26 +27,30 @@ const expectToBeCase = (node, arg) =>
   expectCase(node) &&
   methodName(node) === 'toBe' &&
   argument(node) &&
-  argument(node).value === arg;
+  argument(node).value === arg &&
+  (arg === null || argument(node).name);
 
 const expectNotToBeCase = (node, arg) =>
   expectNotCase(node) &&
   methodName2(node) === 'toBe' &&
   argument2(node) &&
-  argument2(node).value === arg;
+  argument2(node).value === arg &&
+  (arg === null || argument2(node).name);
 
 const expectToEqualCase = (node, arg) =>
   !(expectNotCase(node) || expectResolveCase(node) || expectRejectCase(node)) &&
   expectCase(node) &&
   methodName(node) === 'toEqual' &&
   argument(node) &&
-  argument(node).value === arg;
+  argument(node).value === arg &&
+  (arg === null || argument(node).name);
 
 const expectNotToEqualCase = (node, arg) =>
   expectNotCase(node) &&
   methodName2(node) === 'toEqual' &&
   argument2(node) &&
-  argument2(node).value === arg;
+  argument2(node).value === arg &&
+  (arg === null || argument2(node).name);
 
 const expectToBeUndefinedCase = node =>
   !(expectNotCase(node) || expectResolveCase(node) || expectRejectCase(node)) &&