diff --git a/integration/tests/overlay-focus-trap.test.js b/integration/tests/overlay-focus-trap.test.js
index bf0ca27ac0..220c48a6a9 100644
--- a/integration/tests/overlay-focus-trap.test.js
+++ b/integration/tests/overlay-focus-trap.test.js
@@ -32,6 +32,8 @@ describe('focus-trap', () => {
         }
       };
       overlay.requestContentUpdate();
+      overlay.opened = true;
+      await oneEvent(overlay, 'vaadin-overlay-open');
       focusableElements = getFocusableElements(overlay.$.overlay);
     });
 
@@ -49,10 +51,7 @@ describe('focus-trap', () => {
       expect(focusableElements[5]).to.equal(overlay.querySelector('vaadin-button'));
     });
 
-    it('should focus focusable elements inside the content when focusTrap = true', async () => {
-      overlay.opened = true;
-      await oneEvent(overlay, 'vaadin-overlay-open');
-
+    it('should focus focusable elements inside the content when focusTrap = true', () => {
       // Tab
       for (let i = 0; i < focusableElements.length; i++) {
         const focusedIndex = getFocusedElementIndex();
@@ -88,10 +87,12 @@ describe('focus-trap', () => {
         }
       };
       overlay.requestContentUpdate();
-      focusableElements = getFocusableElements(overlay.$.overlay);
     });
 
-    it('should properly detect multiple focusable elements inside shadow DOM', () => {
+    it('should properly detect multiple focusable elements inside shadow DOM', async () => {
+      overlay.opened = true;
+      await oneEvent(overlay, 'vaadin-overlay-open');
+      focusableElements = getFocusableElements(overlay.$.overlay);
       expect(focusableElements.length).to.equal(4);
       const div = overlay.querySelector('div');
       expect(focusableElements[1]).to.equal(div.shadowRoot.querySelector('input'));
@@ -101,6 +102,7 @@ describe('focus-trap', () => {
     it('should not focus the overlay part if the content is already focused', async () => {
       overlay.opened = true;
       // Needs to happen after opened and before focus-trap loop is executed
+      focusableElements = getFocusableElements(overlay.$.overlay);
       focusableElements[1].focus();
       await oneEvent(overlay, 'vaadin-overlay-open');
       expect(getFocusedElementIndex()).not.to.equal(0);
@@ -108,8 +110,9 @@ describe('focus-trap', () => {
 
     it('should focus first element with tabIndex=1', async () => {
       // It's an arguable behavior, probably overlay should be focused instead
-      focusableElements[1].tabIndex = 1;
       overlay.opened = true;
+      focusableElements = getFocusableElements(overlay.$.overlay);
+      focusableElements[1].tabIndex = 1;
       await oneEvent(overlay, 'vaadin-overlay-open');
       const idx = getFocusedElementIndex();
       expect(focusableElements[idx].tabIndex).to.equal(1);
@@ -118,6 +121,7 @@ describe('focus-trap', () => {
     it('should focus focusable elements in shadow DOM on Tab and Shift Tab', async () => {
       overlay.opened = true;
       await oneEvent(overlay, 'vaadin-overlay-open');
+      focusableElements = getFocusableElements(overlay.$.overlay);
 
       // Tab
       for (let i = 0; i < focusableElements.length; i++) {
diff --git a/packages/dialog/test/dialog.common.js b/packages/dialog/test/dialog.common.js
index 4f028b384d..3739484e04 100644
--- a/packages/dialog/test/dialog.common.js
+++ b/packages/dialog/test/dialog.common.js
@@ -145,10 +145,11 @@ describe('vaadin-dialog', () => {
       it('should restore opened state when added to the DOM', async () => {
         const parent = dialog.parentNode;
         dialog.remove();
-        await aTimeout(0);
+        await nextRender();
         expect(dialog.opened).to.be.false;
 
         parent.appendChild(dialog);
+        await nextRender();
         expect(dialog.opened).to.be.true;
       });
 
@@ -202,11 +203,13 @@ describe('vaadin-dialog', () => {
       await nextRender();
     });
 
-    it('should not throw an exception if renderer is not present', () => {
-      const openDialog = () => {
+    it('should not throw an exception if renderer is not present', async () => {
+      try {
         dialog.opened = true;
-      };
-      expect(openDialog).to.not.throw();
+        await nextRender();
+      } catch (e) {
+        expect.fail(`Error when opening dialog: ${e}`);
+      }
     });
 
     it('should have min-width for content', async () => {
diff --git a/packages/overlay/src/vaadin-overlay-styles.js b/packages/overlay/src/vaadin-overlay-styles.js
index 19591981ee..193eeed36b 100644
--- a/packages/overlay/src/vaadin-overlay-styles.js
+++ b/packages/overlay/src/vaadin-overlay-styles.js
@@ -39,7 +39,8 @@ export const overlayStyles = css`
   }
 
   :host([hidden]),
-  :host(:not([opened]):not([closing])) {
+  :host(:not([opened]):not([closing])),
+  :host(:not([opened]):not([closing])) [part='overlay'] {
     display: none !important;
   }
 
diff --git a/packages/overlay/test/focus-trap.common.js b/packages/overlay/test/focus-trap.common.js
index 0c7d1badb4..c28954636d 100644
--- a/packages/overlay/test/focus-trap.common.js
+++ b/packages/overlay/test/focus-trap.common.js
@@ -28,6 +28,8 @@ describe('focus-trap', () => {
       await nextRender();
       overlayPart = overlay.$.overlay;
       overlay.requestContentUpdate();
+      overlay.opened = true;
+      await oneEvent(overlay, 'vaadin-overlay-open');
       focusableElements = getFocusableElements(overlayPart);
     });
 
@@ -45,10 +47,7 @@ describe('focus-trap', () => {
       expect(focusableElements[4]).to.equal(overlay.querySelector('input'));
     });
 
-    it('should focus focusable elements inside the content when focusTrap = true', async () => {
-      overlay.opened = true;
-      await oneEvent(overlay, 'vaadin-overlay-open');
-
+    it('should focus focusable elements inside the content when focusTrap = true', () => {
       // Tab
       for (let i = 0; i < focusableElements.length; i++) {
         const focusedIndex = getFocusedElementIndex();
@@ -68,10 +67,7 @@ describe('focus-trap', () => {
       expect(getFocusedElementIndex()).to.equal(focusableElements.length - 1);
     });
 
-    it('should update focus sequence when focusing a random element', async () => {
-      overlay.opened = true;
-      await oneEvent(overlay, 'vaadin-overlay-open');
-
+    it('should update focus sequence when focusing a random element', () => {
       tabKeyDown(document.body);
       expect(getFocusedElementIndex()).to.equal(1);
 
@@ -83,15 +79,16 @@ describe('focus-trap', () => {
 
   describe('empty', () => {
     beforeEach(async () => {
-      overlay = fixtureSync('<vaadin-overlay focus-trap></vaadin-overlay>');
+      overlay = fixtureSync('<vaadin-overlay></vaadin-overlay>');
       await nextRender();
       overlayPart = overlay.$.overlay;
-      focusableElements = getFocusableElements(overlayPart);
     });
 
     it('should focus the overlay part when focusTrap = true', async () => {
+      overlay.focusTrap = true;
       overlay.opened = true;
       await oneEvent(overlay, 'vaadin-overlay-open');
+      focusableElements = getFocusableElements(overlayPart);
       expect(focusableElements[0]).to.equal(overlayPart);
       expect(getFocusedElementIndex()).to.equal(0);
     });
@@ -100,6 +97,7 @@ describe('focus-trap', () => {
       overlay.focusTrap = false;
       overlay.opened = true;
       await oneEvent(overlay, 'vaadin-overlay-open');
+      focusableElements = getFocusableElements(overlayPart);
       expect(getFocusedElementIndex()).to.equal(-1);
     });
   });