diff --git a/events.js b/events.js
index edd45ce..34b69a0 100644
--- a/events.js
+++ b/events.js
@@ -448,29 +448,50 @@ function unwrapListeners(arr) {
 
 function once(emitter, name) {
   return new Promise(function (resolve, reject) {
-    function eventListener() {
-      if (errorListener !== undefined) {
+    function errorListener(err) {
+      emitter.removeListener(name, resolver);
+      reject(err);
+    }
+
+    function resolver() {
+      if (typeof emitter.removeListener === 'function') {
         emitter.removeListener('error', errorListener);
       }
       resolve([].slice.call(arguments));
     };
-    var errorListener;
-
-    // Adding an error listener is not optional because
-    // if an error is thrown on an event emitter we cannot
-    // guarantee that the actual event we are waiting will
-    // be fired. The result could be a silent way to create
-    // memory or file descriptor leaks, which is something
-    // we should avoid.
-    if (name !== 'error') {
-      errorListener = function errorListener(err) {
-        emitter.removeListener(name, eventListener);
-        reject(err);
-      };
 
-      emitter.once('error', errorListener);
+    eventTargetAgnosticAddListener(emitter, name, resolver, { once: true });
+    if (name !== 'error') {
+      addErrorHandlerIfEventEmitter(emitter, errorListener, { once: true });
     }
-
-    emitter.once(name, eventListener);
   });
 }
+
+function addErrorHandlerIfEventEmitter(emitter, handler, flags) {
+  if (typeof emitter.on === 'function') {
+    eventTargetAgnosticAddListener(emitter, 'error', handler, flags);
+  }
+}
+
+function eventTargetAgnosticAddListener(emitter, name, listener, flags) {
+  if (typeof emitter.on === 'function') {
+    if (flags.once) {
+      emitter.once(name, listener);
+    } else {
+      emitter.on(name, listener);
+    }
+  } else if (typeof emitter.addEventListener === 'function') {
+    // EventTarget does not have `error` event semantics like Node
+    // EventEmitters, we do not listen for `error` events here.
+    emitter.addEventListener(name, function wrapListener(arg) {
+      // IE does not have builtin `{ once: true }` support so we
+      // have to do it manually.
+      if (flags.once) {
+        emitter.removeEventListener(name, wrapListener);
+      }
+      listener(arg);
+    });
+  } else {
+    throw new TypeError('The "emitter" argument must be of type EventEmitter. Received type ' + typeof emitter);
+  }
+}
diff --git a/package.json b/package.json
index d936726..9810e97 100644
--- a/package.json
+++ b/package.json
@@ -24,6 +24,7 @@
   "devDependencies": {
     "airtap": "^1.0.0",
     "functions-have-names": "^1.2.1",
+    "has": "^1.0.3",
     "has-symbols": "^1.0.1",
     "isarray": "^2.0.5",
     "tape": "^5.0.0"
diff --git a/tests/events-once.js b/tests/events-once.js
index 309bf45..dae8649 100644
--- a/tests/events-once.js
+++ b/tests/events-once.js
@@ -3,8 +3,62 @@
 var common = require('./common');
 var EventEmitter = require('../').EventEmitter;
 var once = require('../').once;
+var has = require('has');
 var assert = require('assert');
 
+function Event(type) {
+  this.type = type;
+}
+
+function EventTargetMock() {
+  this.events = {};
+
+  this.addEventListener = common.mustCall(this.addEventListener);
+  this.removeEventListener = common.mustCall(this.removeEventListener);
+}
+
+EventTargetMock.prototype.addEventListener = function addEventListener(name, listener, options) {
+  if (!(name in this.events)) {
+    this.events[name] = { listeners: [], options: options || {} }
+  }
+  this.events[name].listeners.push(listener);
+};
+
+EventTargetMock.prototype.removeEventListener = function removeEventListener(name, callback) {
+  if (!(name in this.events)) {
+    return;
+  }
+  var event = this.events[name];
+  var stack = event.listeners;
+
+  for (var i = 0, l = stack.length; i < l; i++) {
+    if (stack[i] === callback) {
+      stack.splice(i, 1);
+      if (stack.length === 0) {
+        delete this.events[name];
+      }
+      return;
+    }
+  }
+};
+
+EventTargetMock.prototype.dispatchEvent = function dispatchEvent(arg) {
+  if (!(arg.type in this.events)) {
+    return true;
+  }
+
+  var event = this.events[arg.type];
+  var stack = event.listeners.slice();
+
+  for (var i = 0, l = stack.length; i < l; i++) {
+    stack[i].call(null, arg);
+    if (event.options.once) {
+      this.removeEventListener(arg.type, stack[i]);
+    }
+  }
+  return !arg.defaultPrevented;
+};
+
 function onceAnEvent() {
   var ee = new EventEmitter();
 
@@ -80,7 +134,9 @@ function onceError() {
     ee.emit('error', expected);
   });
 
-  return once(ee, 'error').then(function (args) {
+  var promise = once(ee, 'error');
+  assert.strictEqual(ee.listenerCount('error'), 1);
+  return promise.then(function (args) {
     var err = args[0]
     assert.strictEqual(err, expected);
     assert.strictEqual(ee.listenerCount('error'), 0);
@@ -88,13 +144,91 @@ function onceError() {
   });
 }
 
-Promise.all([
+function onceWithEventTarget() {
+  var et = new EventTargetMock();
+  var event = new Event('myevent');
+  process.nextTick(function () {
+    et.dispatchEvent(event);
+  });
+  return once(et, 'myevent').then(function (args) {
+    var value = args[0];
+    assert.strictEqual(value, event);
+    assert.strictEqual(has(et.events, 'myevent'), false);
+  });
+}
+
+function onceWithEventTargetError() {
+  var et = new EventTargetMock();
+  var error = new Event('error');
+  process.nextTick(function () {
+    et.dispatchEvent(error);
+  });
+  return once(et, 'error').then(function (args) {
+    var err = args[0];
+    assert.strictEqual(err, error);
+    assert.strictEqual(has(et.events, 'error'), false);
+  });
+}
+
+function prioritizesEventEmitter() {
+  var ee = new EventEmitter();
+  ee.addEventListener = assert.fail;
+  ee.removeAllListeners = assert.fail;
+  process.nextTick(function () {
+    ee.emit('foo');
+  });
+  return once(ee, 'foo');
+}
+
+var allTests = [
   onceAnEvent(),
   onceAnEventWithTwoArgs(),
   catchesErrors(),
   stopListeningAfterCatchingError(),
-  onceError()
-]).catch(function (err) {
-  console.error(err.stack)
-  process.exit(1)
-});
+  onceError(),
+  onceWithEventTarget(),
+  onceWithEventTargetError(),
+  prioritizesEventEmitter()
+];
+
+var hasBrowserEventTarget = false;
+try {
+  hasBrowserEventTarget = typeof (new window.EventTarget().addEventListener) === 'function' &&
+    new window.Event('xyz').type === 'xyz';
+} catch (err) {}
+
+if (hasBrowserEventTarget) {
+  var onceWithBrowserEventTarget = function onceWithBrowserEventTarget() {
+    var et = new window.EventTarget();
+    var event = new window.Event('myevent');
+    process.nextTick(function () {
+      et.dispatchEvent(event);
+    });
+    return once(et, 'myevent').then(function (args) {
+      var value = args[0];
+      assert.strictEqual(value, event);
+      assert.strictEqual(has(et.events, 'myevent'), false);
+    });
+  }
+
+  var onceWithBrowserEventTargetError = function onceWithBrowserEventTargetError() {
+    var et = new window.EventTarget();
+    var error = new window.Event('error');
+    process.nextTick(function () {
+      et.dispatchEvent(error);
+    });
+    return once(et, 'error').then(function (args) {
+      var err = args[0];
+      assert.strictEqual(err, error);
+      assert.strictEqual(has(et.events, 'error'), false);
+    });
+  }
+
+  common.test.comment('Testing with browser built-in EventTarget');
+  allTests.push([
+    onceWithBrowserEventTarget(),
+    onceWithBrowserEventTargetError()
+  ]);
+}
+
+module.exports = Promise.all(allTests);
diff --git a/tests/index.js b/tests/index.js
index 491d0b8..2d739e6 100644
--- a/tests/index.js
+++ b/tests/index.js
@@ -14,7 +14,15 @@ var require = function(file) {
         t.on('end', function () { delete common.test; });
         common.test = t;
 
-        try { orig_require(file); } catch (err) { t.fail(err); }
+        try {
+          var exp = orig_require(file);
+          if (exp && exp.then) {
+            exp.then(function () { t.end(); }, t.fail);
+            return;
+          }
+        } catch (err) {
+          t.fail(err);
+        }
         t.end();
     });
 };