diff --git a/.travis.yml b/.travis.yml
index 22b54e2f..b7316fff 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -21,18 +21,10 @@ matrix:
       env: BROWSER='"firefox_61"' OPENPGPJSTEST='browserstack'
     - node_js: "10"
       env:  BROWSER='"chrome_68"' OPENPGPJSTEST='browserstack' LIGHTWEIGHT=1
-    - node_js: "9"
-      env: BROWSER='"chrome_49"' OPENPGPJSTEST='browserstack' COMPAT=1
     - node_js: "10"
       env: BROWSER='"chrome_68"' OPENPGPJSTEST='browserstack'
-    - node_js: "9"
-      env: BROWSER='"safari_9_1"' OPENPGPJSTEST='browserstack' COMPAT=1
-    - node_js: "9"
-      env: BROWSER='"safari_10_1"' OPENPGPJSTEST='browserstack' COMPAT=1
     - node_js: "9"
       env: BROWSER='"safari_11_1"' OPENPGPJSTEST='browserstack'
-    - node_js: "9"
-      env: BROWSER='{"os":"ios", "os_version":"10.3", "device":"iPhone 7 Plus", "real_mobile":true}' OPENPGPJSTEST='browserstack' COMPAT=1
     - node_js: "9"
       env: BROWSER='{"os":"ios", "os_version":"11.3", "device":"iPhone 8 Plus", "real_mobile":true}' OPENPGPJSTEST='browserstack'
   allow_failures:
diff --git a/README.md b/README.md
index 77e75cf7..80002b2a 100644
--- a/README.md
+++ b/README.md
@@ -40,10 +40,6 @@ OpenPGP.js [![Build Status](https://travis-ci.org/openpgpjs/openpgpjs.svg?branch
 
 * The `dist/openpgp.min.js` bundle works well with recent versions of Chrome, Firefox, Safari and Edge. It also works in Node.js 8+.
 
-* The `dist/compat/openpgp.min.js` bundle also works with Internet Explorer 11 and old versions of Safari. Please note that this bundle overwrites the global `Promise` with a polyfill version even in some cases where it already exists, which may cause issues. It also adds some built-in prototype functions if they don't exist, such as `Array.prototype.includes`.
-
-* If you wish, you could even load one or the other depending on which browser the user is using.
-
 * Currently, Chrome, Safari and Edge have partial implementations of the
 [Streams specification](https://streams.spec.whatwg.org/), and Firefox
 has a partial implementation behind feature flags. Chrome is the only
diff --git a/package-lock.json b/package-lock.json
index 5c9fd873..7575ccc1 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -760,12 +760,6 @@
         "safe-buffer": "~5.1.1"
       }
     },
-    "core-js": {
-      "version": "2.5.3",
-      "resolved": "https://registry.npmjs.org/core-js/-/core-js-2.5.3.tgz",
-      "integrity": "sha1-isw4NFgk8W2DZbfJtCWRaOjtYD4=",
-      "dev": true
-    },
     "core-util-is": {
       "version": "1.0.2",
       "resolved": "https://registry.npmjs.org/core-util-is/-/core-util-is-1.0.2.tgz",
diff --git a/package.json b/package.json
index b5a8c3e0..d6ab7c93 100644
--- a/package.json
+++ b/package.json
@@ -52,7 +52,6 @@
     "buffer": "^5.0.8",
     "chai": "^4.1.2",
     "chai-as-promised": "^7.1.1",
-    "core-js": "^2.5.3",
     "elliptic": "github:openpgpjs/elliptic#ab7d8268c60b6abeb175841c578c224ac5b2d279",
     "email-addresses": "3.1.0",
     "eslint": "^4.17.0",
diff --git a/rollup.config.js b/rollup.config.js
index a108b024..4a0e830f 100644
--- a/rollup.config.js
+++ b/rollup.config.js
@@ -9,19 +9,6 @@ import pkg from './package.json';
 
 const nodeDependencies = Object.keys(pkg.dependencies);
 
-const compat = [
-  'whatwg-fetch',
-  'core-js/fn/array/fill',
-  'core-js/fn/array/find',
-  'core-js/fn/array/includes',
-  'core-js/fn/array/from',
-  'core-js/fn/promise',
-  'core-js/fn/typed/uint8-array',
-  'core-js/fn/string/repeat',
-  'core-js/fn/symbol',
-  'core-js/fn/object/assign'
-];
-
 const banner =
   `/*! OpenPGP.js v${pkg.version} - ` +
   `${new Date().toISOString().split('T')[0]} - ` +
@@ -48,7 +35,7 @@ export default [
         browser: true
       }),
       commonjs({
-        ignore: builtinModules.concat(nodeDependencies).concat(compat)
+        ignore: builtinModules.concat(nodeDependencies)
       }),
       replace({
         'OpenPGP.js VERSION': `OpenPGP.js ${pkg.version}`,
@@ -68,9 +55,7 @@ export default [
     ],
     plugins: [
       resolve(),
-      commonjs({
-        ignore: compat
-      }),
+      commonjs(),
       replace({
         'OpenPGP.js VERSION': `OpenPGP.js ${pkg.version}`,
       })
@@ -89,7 +74,7 @@ export default [
         browser: true
       }),
       commonjs({
-        ignore: builtinModules.concat(nodeDependencies).concat(compat).concat('elliptic')
+        ignore: builtinModules.concat(nodeDependencies).concat('elliptic')
       }),
       replace({
         'OpenPGP.js VERSION': `OpenPGP.js ${pkg.version}`,
@@ -121,7 +106,7 @@ export default [
         browser: true
       }),
       commonjs({
-        ignore: builtinModules.concat(nodeDependencies).concat(compat).concat(['../..', '../../..'])
+        ignore: builtinModules.concat(nodeDependencies).concat(['../..', '../../..'])
       })
     ]
   }
diff --git a/src/polyfills.js b/src/polyfills.js
index 630b286f..1642ee31 100644
--- a/src/polyfills.js
+++ b/src/polyfills.js
@@ -1,51 +1,7 @@
 /**
- * @fileoverview Old browser polyfills
- * All are listed as dev dependencies because Node does not need them
- * and for browser babel will take care of it
  * @module polyfills
  */
 
-if (typeof globalThis !== 'undefined') {
-  /********************************************************************
-   * NOTE: This list is duplicated in Gruntfile.js,                   *
-   * so that these polyfills are only included in the compat bundle.  *
-   ********************************************************************/
-
-  try {
-    if (typeof globalThis.fetch === 'undefined') {
-      require('whatwg-fetch');
-    }
-    if (typeof Array.prototype.fill === 'undefined') {
-      require('core-js/fn/array/fill');
-    }
-    if (typeof Array.prototype.find === 'undefined') {
-      require('core-js/fn/array/find');
-    }
-    if (typeof Array.prototype.includes === 'undefined') {
-      require('core-js/fn/array/includes');
-    }
-    if (typeof Array.from === 'undefined') {
-      require('core-js/fn/array/from');
-    }
-
-    // No if-statement on Promise because of IE11. Otherwise Promise is undefined in the service worker.
-    require('core-js/fn/promise');
-
-    if (typeof Uint8Array.from === 'undefined') {
-      require('core-js/fn/typed/uint8-array');
-    }
-    if (typeof String.prototype.repeat === 'undefined') {
-      require('core-js/fn/string/repeat');
-    }
-    if (typeof Symbol === 'undefined') {
-      require('core-js/fn/symbol');
-    }
-    if (typeof Object.assign === 'undefined') {
-      require('core-js/fn/object/assign');
-    }
-  } catch (e) {}
-}
-
 if (typeof TextEncoder === 'undefined') {
   const nodeUtil = require('util') || {};
   globalThis.TextEncoder = nodeUtil.TextEncoder;
diff --git a/test/unittests.js b/test/unittests.js
index 8897b008..3aaa9c16 100644
--- a/test/unittests.js
+++ b/test/unittests.js
@@ -1,11 +1,3 @@
-// Old browser polyfills
-if (typeof Symbol === 'undefined') {
-  require('core-js/fn/symbol');
-}
-if (typeof Promise === 'undefined') {
-  require('core-js/fn/promise');
-}
-
 (typeof window !== 'undefined' ? window : global).resolves = function(val) {
   return new Promise(function(res) { res(val); });
 };