diff --git a/README.md b/README.md
index c1f89f526..c0d9b0e19 100644
--- a/README.md
+++ b/README.md
@@ -24,7 +24,7 @@ Feel free to stop by our [Matrix room](https://chat.mozilla.org/#/room/#pdfjs:mo
 ### Online demo
 
 Please note that the "Modern browsers" version assumes native support for
-features such as e.g. `async`/`await`, `Promise`, and `ReadableStream`.
+features such as e.g. `async`/`await`, and `ReadableStream`.
 
 + Modern browsers: https://mozilla.github.io/pdf.js/web/viewer.html
 
diff --git a/external/dist/README.md b/external/dist/README.md
index 66c1ef1ff..6baa2e580 100644
--- a/external/dist/README.md
+++ b/external/dist/README.md
@@ -8,7 +8,6 @@ This is a pre-built version of the PDF.js source code. It is automatically
 generated by the build scripts.
 
 For usage with older browsers/environments, without support for modern features
-such as e.g. `async`/`await`, `Promise`, and `ReadableStream`,
-please refer to the `es5` folder.
+such as e.g. `async`/`await`, and `ReadableStream`, please see the `es5` folder.
 
 See https://github.com/mozilla/pdf.js for learning and contributing.
diff --git a/src/shared/compatibility.js b/src/shared/compatibility.js
index 8e3d11a0e..05bec1e95 100644
--- a/src/shared/compatibility.js
+++ b/src/shared/compatibility.js
@@ -242,14 +242,16 @@ if (
     require("core-js/es/typed-array/slice");
   })();
 
-  // Support: IE, Safari<11, Chrome<63
+  // Provides support for *recent* additions to the Promise specification,
+  // however basic Promise support is assumed to be available natively.
+  // Support: Firefox<71, Safari<13, Chrome<76
   (function checkPromise() {
     if (typeof PDFJSDev !== "undefined" && PDFJSDev.test("IMAGE_DECODERS")) {
       // The current image decoders are synchronous, hence `Promise` shouldn't
       // need to be polyfilled for the IMAGE_DECODERS build target.
       return;
     }
-    if (globalThis.Promise && globalThis.Promise.allSettled) {
+    if (globalThis.Promise.allSettled) {
       return;
     }
     globalThis.Promise = require("core-js/es/promise/index.js");