diff --git a/experimental/puppeteer-firefox/lib/ExecutionContext.js b/experimental/puppeteer-firefox/lib/ExecutionContext.js
index e00ee1ec2dc..828924c5122 100644
--- a/experimental/puppeteer-firefox/lib/ExecutionContext.js
+++ b/experimental/puppeteer-firefox/lib/ExecutionContext.js
@@ -21,9 +21,34 @@ class ExecutionContext {
       });
       return createHandle(this, payload.result, payload.exceptionDetails);
     }
+    if (typeof pageFunction !== 'function')
+      throw new Error(`Expected to get |string| or |function| as the first argument, but got "${pageFunction}" instead.`);
+
+    let functionText = pageFunction.toString();
+    try {
+      new Function('(' + functionText + ')');
+    } catch (e1) {
+      // This means we might have a function shorthand. Try another
+      // time prefixing 'function '.
+      if (functionText.startsWith('async '))
+        functionText = 'async function ' + functionText.substring('async '.length);
+      else
+        functionText = 'function ' + functionText;
+      try {
+        new Function('(' + functionText  + ')');
+      } catch (e2) {
+        // We tried hard to serialize, but there's a weird beast here.
+        throw new Error('Passed function is not well-serializable!');
+      }
+    }
     args = args.map(arg => {
-      if (arg instanceof JSHandle)
+      if (arg instanceof JSHandle) {
+        if (arg._context !== this)
+          throw new Error('JSHandles can be evaluated only in the context they were created!');
+        if (arg._disposed)
+          throw new Error('JSHandle is disposed!');
         return arg._protocolValue;
+      }
       if (Object.is(arg, Infinity))
         return {unserializableValue: 'Infinity'};
       if (Object.is(arg, -Infinity))
@@ -35,7 +60,7 @@ class ExecutionContext {
       return {value: arg};
     });
     const payload = await this._session.send('Page.evaluate', {
-      functionText: pageFunction.toString(),
+      functionText,
       args,
       executionContextId: this._executionContextId
     });
diff --git a/experimental/puppeteer-firefox/lib/JSHandle.js b/experimental/puppeteer-firefox/lib/JSHandle.js
index fb735eff9f2..a0aa95ff27c 100644
--- a/experimental/puppeteer-firefox/lib/JSHandle.js
+++ b/experimental/puppeteer-firefox/lib/JSHandle.js
@@ -13,6 +13,7 @@ class JSHandle {
     this._objectId = payload.objectId;
     this._type = payload.type;
     this._subtype = payload.subtype;
+    this._disposed = false;
     this._protocolValue = {
       unserializableValue: payload.unserializableValue,
       value: payload.value,
@@ -102,6 +103,7 @@ class JSHandle {
   async dispose() {
     if (!this._objectId)
       return;
+    this._disposed = true;
     await this._session.send('Page.disposeObject', {
       executionContextId: this._executionContextId,
       objectId: this._objectId,
diff --git a/lib/ExecutionContext.js b/lib/ExecutionContext.js
index 2a6c9ac2274..8372fbae017 100644
--- a/lib/ExecutionContext.js
+++ b/lib/ExecutionContext.js
@@ -82,7 +82,7 @@ class ExecutionContext {
     }
 
     if (typeof pageFunction !== 'function')
-      throw new Error('The following is not a function: ' + pageFunction);
+      throw new Error(`Expected to get |string| or |function| as the first argument, but got "${pageFunction}" instead.`);
 
     let functionText = pageFunction.toString();
     try {
diff --git a/test/evaluation.spec.js b/test/evaluation.spec.js
index bc1d912f4a7..d03b4f5d205 100644
--- a/test/evaluation.spec.js
+++ b/test/evaluation.spec.js
@@ -68,7 +68,7 @@ module.exports.addTests = function({testRunner, expect}) {
     it_fails_ffox('should return undefined for objects with symbols', async({page, server}) => {
       expect(await page.evaluate(() => [Symbol('foo4')])).toBe(undefined);
     });
-    (asyncawait ? it_fails_ffox : xit)('should work with function shorthands', async({page, server}) => {
+    (asyncawait ? it : xit)('should work with function shorthands', async({page, server}) => {
       // trick node6 transpiler to not touch our object.
       // TODO(lushnikov): remove eval once Node6 is dropped.
       const a = eval(`({
@@ -188,7 +188,7 @@ module.exports.addTests = function({testRunner, expect}) {
       const text = await page.evaluate(e => e.textContent, element);
       expect(text).toBe('42');
     });
-    it_fails_ffox('should throw if underlying element was disposed', async({page, server}) => {
+    it('should throw if underlying element was disposed', async({page, server}) => {
       await page.setContent('<section>39</section>');
       const element = await page.$('section');
       expect(element).toBeTruthy();
@@ -197,7 +197,7 @@ module.exports.addTests = function({testRunner, expect}) {
       await page.evaluate(e => e.textContent, element).catch(e => error = e);
       expect(error.message).toContain('JSHandle is disposed');
     });
-    it_fails_ffox('should throw if elementHandles are from other frames', async({page, server}) => {
+    it('should throw if elementHandles are from other frames', async({page, server}) => {
       await utils.attachFrame(page, 'frame1', server.EMPTY_PAGE);
       const bodyHandle = await page.frames()[1].$('body');
       let error = null;