diff --git a/test/browsercontext.spec.js b/test/browsercontext.spec.js
index 76d8a4168b..9d9eea4334 100644
--- a/test/browsercontext.spec.js
+++ b/test/browsercontext.spec.js
@@ -446,7 +446,7 @@ describe('BrowserContext.route', () => {
 });
 
 describe('BrowserContext.setHTTPCredentials', function() {
-  it('should work', async({browser, server}) => {
+  it.fail(CHROMIUM && !HEADLESS)('should work', async({browser, server}) => {
     server.setAuth('/empty.html', 'user', 'pass');
     const context = await browser.newContext();
     const page = await context.newPage();
@@ -476,7 +476,7 @@ describe('BrowserContext.setHTTPCredentials', function() {
     expect(response.status()).toBe(200);
     await context.close();
   });
-  it('should allow disable authentication', async({browser, server}) => {
+  it.fail(CHROMIUM && !HEADLESS)('should allow disable authentication', async({browser, server}) => {
     server.setAuth('/empty.html', 'user', 'pass');
     const context = await browser.newContext({
       httpCredentials: { username: 'user', password: 'pass' }
diff --git a/test/download.spec.js b/test/download.spec.js
index 5f09430feb..0deefda6b5 100644
--- a/test/download.spec.js
+++ b/test/download.spec.js
@@ -123,7 +123,7 @@ describe('Download', function() {
     expect(fs.readFileSync(path).toString()).toBe('Hello world');
     await page.close();
   });
-  it('should report new window downloads', async({browser, server}) => {
+  it.fail(CHROMIUM && !HEADLESS)('should report new window downloads', async({browser, server}) => {
     // TODO: - the test fails in headful Chromium as the popup page gets closed along
     // with the session before download completed event arrives.
     // - WebKit doesn't close the popup page
diff --git a/test/elementhandle.spec.js b/test/elementhandle.spec.js
index fe6f3bd00d..91033e8103 100644
--- a/test/elementhandle.spec.js
+++ b/test/elementhandle.spec.js
@@ -19,7 +19,7 @@ const utils = require('./utils');
 const {FFOX, CHROMIUM, WEBKIT} = require('./utils').testOptions(browserType);
 
 describe('ElementHandle.boundingBox', function() {
-  it('should work', async({page, server}) => {
+  it.fail(FFOX && !HEADLESS)('should work', async({page, server}) => {
     await page.setViewportSize({width: 500, height: 500});
     await page.goto(server.PREFIX + '/grid.html');
     const elementHandle = await page.$('.box:nth-of-type(13)');
diff --git a/test/fixtures.spec.js b/test/fixtures.spec.js
index 4b44bc283f..86c0fa5c43 100644
--- a/test/fixtures.spec.js
+++ b/test/fixtures.spec.js
@@ -73,7 +73,7 @@ describe('Fixtures', function() {
     // so we don't check it here.
   });
 
-  describe.skip(WIN)('signals', () => {
+  describe.skip(WIN).skip(!HEADLESS)('signals', () => {
     // Cannot reliably send signals on Windows.
     it.slow()('should report browser close signal', async state => {
       const result = await testSignal(state, (child, browserPid) => process.kill(browserPid), true);
diff --git a/test/permissions.spec.js b/test/permissions.spec.js
index 60e065ee50..5bf60dcd70 100644
--- a/test/permissions.spec.js
+++ b/test/permissions.spec.js
@@ -85,7 +85,7 @@ describe.skip(WEBKIT)('Permissions', function() {
   //TODO: flaky
   // - Linux: https://github.com/microsoft/playwright/pull/1790/checks?check_run_id=587327883
   // - Win: https://ci.appveyor.com/project/aslushnikov/playwright/builds/32402536
-  it.fail(FFOX)('should trigger permission onchange', async({page, server, context}) => {
+  it.fail(FFOX).fail(CHROMIUM && !HEADLESS)('should trigger permission onchange', async({page, server, context}) => {
     await page.goto(server.EMPTY_PAGE);
     await page.evaluate(() => {
       window['events'] = [];
@@ -122,7 +122,7 @@ describe.skip(WEBKIT)('Permissions', function() {
     expect(await getPermission(otherPage, 'geolocation')).toBe('granted');
     await otherContext.close();
   });
-  it.skip(FFOX)('should support clipboard read', async({page, server, context, browser}) => {
+  it.skip(FFOX).fail(CHROMIUM && !HEADLESS)('should support clipboard read', async({page, server, context, browser}) => {
     // No such permissions (requires flag) in Firefox
     await page.goto(server.EMPTY_PAGE);
     expect(await getPermission(page, 'clipboard-read')).toBe('prompt');