diff --git a/packages/puppeteer-core/src/common/Browser.ts b/packages/puppeteer-core/src/common/Browser.ts
index 36ebb50e37d..8cb2de51a8d 100644
--- a/packages/puppeteer-core/src/common/Browser.ts
+++ b/packages/puppeteer-core/src/common/Browser.ts
@@ -33,6 +33,7 @@ import {
 import {BrowserContext} from '../api/BrowserContext.js';
 import {Page} from '../api/Page.js';
 import {assert} from '../util/assert.js';
+import {createDeferredPromise} from '../util/DeferredPromise.js';
 
 import {ChromeTargetManager} from './ChromeTargetManager.js';
 import {CDPSession, Connection, ConnectionEmittedEvents} from './Connection.js';
@@ -478,11 +479,8 @@ export class CDPBrowser extends BrowserBase {
     options: WaitForTargetOptions = {}
   ): Promise<Target> {
     const {timeout = 30000} = options;
-    let resolve: (value: Target | PromiseLike<Target>) => void;
-    let isResolved = false;
-    const targetPromise = new Promise<Target>(x => {
-      return (resolve = x);
-    });
+    const targetPromise = createDeferredPromise<Target | PromiseLike<Target>>();
+
     this.on(BrowserEmittedEvents.TargetCreated, check);
     this.on(BrowserEmittedEvents.TargetChanged, check);
     try {
@@ -497,9 +495,8 @@ export class CDPBrowser extends BrowserBase {
     }
 
     async function check(target: Target): Promise<void> {
-      if ((await predicate(target)) && !isResolved) {
-        isResolved = true;
-        resolve(target);
+      if ((await predicate(target)) && !targetPromise.resolved()) {
+        targetPromise.resolve(target);
       }
     }
   }
diff --git a/packages/puppeteer-core/src/common/ChromeTargetManager.ts b/packages/puppeteer-core/src/common/ChromeTargetManager.ts
index 4ba515e48ff..58c8353aadb 100644
--- a/packages/puppeteer-core/src/common/ChromeTargetManager.ts
+++ b/packages/puppeteer-core/src/common/ChromeTargetManager.ts
@@ -18,6 +18,7 @@ import {Protocol} from 'devtools-protocol';
 
 import {TargetFilterCallback} from '../api/Browser.js';
 import {assert} from '../util/assert.js';
+import {createDeferredPromise} from '../util/DeferredPromise.js';
 
 import {CDPSession, Connection} from './Connection.js';
 import {EventEmitter} from './EventEmitter.js';
@@ -80,10 +81,7 @@ export class ChromeTargetManager extends EventEmitter implements TargetManager {
     (event: Protocol.Target.DetachedFromTargetEvent) => void
   > = new WeakMap();
 
-  #initializeCallback = () => {};
-  #initializePromise: Promise<void> = new Promise(resolve => {
-    this.#initializeCallback = resolve;
-  });
+  #initializePromise = createDeferredPromise<void>();
   #targetsIdsForInit: Set<string> = new Set();
 
   constructor(
@@ -381,7 +379,7 @@ export class ChromeTargetManager extends EventEmitter implements TargetManager {
   #finishInitializationIfReady(targetId?: string): void {
     targetId !== undefined && this.#targetsIdsForInit.delete(targetId);
     if (this.#targetsIdsForInit.size === 0) {
-      this.#initializeCallback();
+      this.#initializePromise.resolve();
     }
   }
 
diff --git a/packages/puppeteer-core/src/common/FirefoxTargetManager.ts b/packages/puppeteer-core/src/common/FirefoxTargetManager.ts
index d5c8582072f..745c37d9502 100644
--- a/packages/puppeteer-core/src/common/FirefoxTargetManager.ts
+++ b/packages/puppeteer-core/src/common/FirefoxTargetManager.ts
@@ -18,6 +18,7 @@ import {Protocol} from 'devtools-protocol';
 
 import {TargetFilterCallback} from '../api/Browser.js';
 import {assert} from '../util/assert.js';
+import {createDeferredPromise} from '../util/DeferredPromise.js';
 
 import {CDPSession, Connection} from './Connection.js';
 import {EventEmitter} from './EventEmitter.js';
@@ -87,10 +88,7 @@ export class FirefoxTargetManager
     (event: Protocol.Target.AttachedToTargetEvent) => Promise<void>
   > = new WeakMap();
 
-  #initializeCallback = () => {};
-  #initializePromise: Promise<void> = new Promise(resolve => {
-    this.#initializeCallback = resolve;
-  });
+  #initializePromise = createDeferredPromise<void>();
   #targetsIdsForInit: Set<string> = new Set();
 
   constructor(
@@ -255,7 +253,7 @@ export class FirefoxTargetManager
   #finishInitializationIfReady(targetId: string): void {
     this.#targetsIdsForInit.delete(targetId);
     if (this.#targetsIdsForInit.size === 0) {
-      this.#initializeCallback();
+      this.#initializePromise.resolve();
     }
   }
 }
diff --git a/packages/puppeteer-core/src/common/Frame.ts b/packages/puppeteer-core/src/common/Frame.ts
index 962b85c622c..e9cf97f0bbf 100644
--- a/packages/puppeteer-core/src/common/Frame.ts
+++ b/packages/puppeteer-core/src/common/Frame.ts
@@ -798,17 +798,7 @@ export class Frame {
     }
 
     if (path) {
-      let fs;
-      try {
-        fs = (await import('fs')).promises;
-      } catch (error) {
-        if (error instanceof TypeError) {
-          throw new Error(
-            'Can only pass a file path in a Node-like environment.'
-          );
-        }
-        throw error;
-      }
+      const fs = await importFSPromises();
       content = await fs.readFile(path, 'utf8');
       content += `//# sourceURL=${path.replace(/\n/g, '')}`;
     }