diff --git a/src/client.js b/src/client.js
index 187944420..8af841c99 100644
--- a/src/client.js
+++ b/src/client.js
@@ -19,6 +19,7 @@ limitations under the License.
 "use strict";
 
 const PushProcessor = require('./pushprocessor');
+import {sleep} from './utils';
 
 /**
  * This is an internal module. See {@link MatrixClient} for the public class.
@@ -3221,7 +3222,7 @@ MatrixClient.prototype.scrollback = function(room, limit, callback) {
     const self = this;
     // wait for a time before doing this request
     // (which may be 0 in order not to special case the code paths)
-    Promise.delay(timeToWaitMs).then(function() {
+    sleep(timeToWaitMs).then(function() {
         return self._createMessagesRequest(
             room.roomId,
             room.oldState.paginationToken,
diff --git a/src/crypto/DeviceList.js b/src/crypto/DeviceList.js
index 94b3140b0..27b1a23e4 100644
--- a/src/crypto/DeviceList.js
+++ b/src/crypto/DeviceList.js
@@ -31,6 +31,7 @@ import DeviceInfo from './deviceinfo';
 import {CrossSigningInfo} from './CrossSigning';
 import olmlib from './olmlib';
 import IndexedDBCryptoStore from './store/indexeddb-crypto-store';
+import {sleep} from '../utils';
 
 
 /* State transition diagram for DeviceList._deviceTrackingStatus
@@ -763,7 +764,7 @@ class DeviceListUpdateSerialiser {
             // this serves as an easy solution for now.
             let prom = Promise.resolve();
             for (const userId of downloadUsers) {
-                prom = prom.delay(5).then(() => {
+                prom = prom.then(sleep(5)).then(() => {
                     return this._processQueryResponseForUser(
                         userId, dk[userId], {
                             master: masterKeys[userId],
diff --git a/src/crypto/index.js b/src/crypto/index.js
index 11b450a8e..7b1dad314 100644
--- a/src/crypto/index.js
+++ b/src/crypto/index.js
@@ -49,6 +49,7 @@ import {
     newUnexpectedMessageError,
     newUnknownMethodError,
 } from './verification/Error';
+import {sleep} from '../utils';
 
 const defaultVerificationMethods = {
     [ScanQRCode.NAME]: ScanQRCode,
@@ -1834,7 +1835,7 @@ Crypto.prototype.scheduleKeyBackupSend = async function(maxDelay = 10000) {
         // requests from different clients hitting the server all at
         // the same time when a new key is sent
         const delay = Math.random() * maxDelay;
-        await Promise.delay(delay);
+        await sleep(delay);
         let numFailures = 0; // number of consecutive failures
         while (1) {
             if (!this.backupKey) {
@@ -1868,7 +1869,7 @@ Crypto.prototype.scheduleKeyBackupSend = async function(maxDelay = 10000) {
             }
             if (numFailures) {
                 // exponential backoff if we have failures
-                await Promise.delay(1000 * Math.pow(2, Math.min(numFailures - 1, 4)));
+                await sleep(1000 * Math.pow(2, Math.min(numFailures - 1, 4)));
             }
         }
     } finally {
diff --git a/src/utils.js b/src/utils.js
index b752299f0..8cab9fbb8 100644
--- a/src/utils.js
+++ b/src/utils.js
@@ -708,3 +708,8 @@ module.exports.ensureNoTrailingSlash = function(url) {
         return url;
     }
 };
+
+// Returns a promise which resolves with a given value after the given number of ms
+module.exports.sleep = (ms, value) => new Promise((resolve => {
+    setTimeout(resolve, ms, value);
+}));