diff --git a/rules/__tests__/expect-expect.test.js b/rules/__tests__/expect-expect.test.js
index cd1c78836..78c5126e0 100644
--- a/rules/__tests__/expect-expect.test.js
+++ b/rules/__tests__/expect-expect.test.js
@@ -23,6 +23,14 @@ ruleTester.run('expect-expect', rule, {
       code: 'it("should return undefined",() => expectSaga(mySaga).returns());',
       options: [{ assertFunctionNames: ['expectSaga'] }],
     },
+    {
+      code: [
+        'test("verifies the function call", () => {',
+        '  td.verify(someFunctionCall())',
+        '})',
+      ].join('\n'),
+      options: [{ assertFunctionNames: ['td.verify'] }],
+    },
   ],
 
   invalid: [
diff --git a/rules/expect-expect.js b/rules/expect-expect.js
index aaceb9a77..85976808b 100644
--- a/rules/expect-expect.js
+++ b/rules/expect-expect.js
@@ -6,6 +6,7 @@
  */
 
 const getDocsUrl = require('./util').getDocsUrl;
+const getNodeName = require('./util').getNodeName;
 
 module.exports = {
   meta: {
@@ -27,22 +28,25 @@ module.exports = {
   },
   create(context) {
     const unchecked = [];
-    const assertFunctionNames =
+    const assertFunctionNames = new Set(
       context.options[0] && context.options[0].assertFunctionNames
         ? context.options[0].assertFunctionNames
-        : ['expect'];
+        : ['expect']
+    );
 
     return {
-      'CallExpression[callee.name=/^it|test$/]'(node) {
-        unchecked.push(node);
-      },
-      [`CallExpression[callee.name=/^${assertFunctionNames.join('|')}$/]`]() {
-        // Return early in case of nested `it` statements.
-        for (const ancestor of context.getAncestors()) {
-          const index = unchecked.indexOf(ancestor);
-          if (index !== -1) {
-            unchecked.splice(index, 1);
-            break;
+      CallExpression(node) {
+        const name = getNodeName(node.callee);
+        if (name === 'it' || name === 'test') {
+          unchecked.push(node);
+        } else if (assertFunctionNames.has(name)) {
+          // Return early in case of nested `it` statements.
+          for (const ancestor of context.getAncestors()) {
+            const index = unchecked.indexOf(ancestor);
+            if (index !== -1) {
+              unchecked.splice(index, 1);
+              break;
+            }
           }
         }
       },
diff --git a/rules/no-disabled-tests.js b/rules/no-disabled-tests.js
index 83bc12dbf..307e643e6 100644
--- a/rules/no-disabled-tests.js
+++ b/rules/no-disabled-tests.js
@@ -1,23 +1,7 @@
 'use strict';
 
 const getDocsUrl = require('./util').getDocsUrl;
-
-function getName(node) {
-  function joinNames(a, b) {
-    return a && b ? `${a}.${b}` : null;
-  }
-
-  switch (node && node.type) {
-    case 'Identifier':
-      return node.name;
-    case 'Literal':
-      return node.value;
-    case 'MemberExpression':
-      return joinNames(getName(node.object), getName(node.property));
-  }
-
-  return null;
-}
+const getNodeName = require('./util').getNodeName;
 
 function collectReferences(scope) {
   const locals = new Set();
@@ -70,7 +54,7 @@ module.exports = {
         });
       },
       CallExpression(node) {
-        const functionName = getName(node.callee);
+        const functionName = getNodeName(node.callee);
 
         switch (functionName) {
           case 'describe.skip':
diff --git a/rules/util.js b/rules/util.js
index 2dd9def8b..35aa005d1 100644
--- a/rules/util.js
+++ b/rules/util.js
@@ -98,10 +98,20 @@ const testCaseNames = Object.assign(Object.create(null), {
 });
 
 const getNodeName = node => {
-  if (node.type === 'MemberExpression') {
-    return `${node.object.name}.${node.property.name}`;
+  function joinNames(a, b) {
+    return a && b ? `${a}.${b}` : null;
   }
-  return node.name;
+
+  switch (node && node.type) {
+    case 'Identifier':
+      return node.name;
+    case 'Literal':
+      return node.value;
+    case 'MemberExpression':
+      return joinNames(getNodeName(node.object), getNodeName(node.property));
+  }
+
+  return null;
 };
 
 const isTestCase = node =>