diff --git a/core/rfb.js b/core/rfb.js
index 074eb519..228aeca4 100644
--- a/core/rfb.js
+++ b/core/rfb.js
@@ -239,9 +239,8 @@ export default class RFB extends EventTargetMixin {
         this._sock.on('message', this._handleMessage.bind(this));
         this._sock.on('error', this._socketError.bind(this));
 
-        // Slight delay of the actual connection so that the caller has
-        // time to set up callbacks
-        setTimeout(this._updateConnectionState.bind(this, 'connecting'));
+        // All prepared, kick off the connection
+        this._updateConnectionState('connecting');
 
         Log.Debug("<< RFB.constructor");
 
@@ -463,29 +462,20 @@ export default class RFB extends EventTargetMixin {
         Log.Debug(">> RFB.connect");
 
         if (this._url) {
-            try {
-                Log.Info(`connecting to ${this._url}`);
-                this._sock.open(this._url, this._wsProtocols);
-            } catch (e) {
-                if (e.name === 'SyntaxError') {
-                    this._fail("Invalid host or port (" + e + ")");
-                } else {
-                    this._fail("Error when opening socket (" + e + ")");
-                }
-            }
+            Log.Info(`connecting to ${this._url}`);
+            this._sock.open(this._url, this._wsProtocols);
         } else {
-            try {
-                Log.Info(`attaching ${this._rawChannel} to Websock`);
-                this._sock.attach(this._rawChannel);
-            } catch (e) {
-                this._fail("Error attaching channel (" + e + ")");
-            }
+            Log.Info(`attaching ${this._rawChannel} to Websock`);
+            this._sock.attach(this._rawChannel);
 
             if (this._sock.readyState === 'closed') {
-                this._fail("Cannot use already closed WebSocket/RTCDataChannel");
+                throw Error("Cannot use already closed WebSocket/RTCDataChannel");
             }
 
             if (this._sock.readyState === 'open') {
+                // FIXME: _socketOpen() can in theory call _fail(), which
+                //        isn't allowed this early, but I'm not sure that can
+                //        happen without a bug messing up our state variables
                 this._socketOpen();
             }
         }
diff --git a/tests/test.rfb.js b/tests/test.rfb.js
index c99edc75..404f7db1 100644
--- a/tests/test.rfb.js
+++ b/tests/test.rfb.js
@@ -151,34 +151,21 @@ describe('Remote Frame Buffer Protocol Client', function () {
                 attach.restore();
             });
 
-            it('should not connect from constructor', function () {
-                new RFB(document.createElement('div'), 'wss://host:8675');
-                expect(open).to.not.have.been.called;
-                this.clock.tick(); // Flush the pending connection
-            });
-
             it('should actually connect to the websocket', function () {
                 new RFB(document.createElement('div'), 'ws://HOST:8675/PATH');
-                this.clock.tick();
                 expect(open).to.have.been.calledOnceWithExactly('ws://HOST:8675/PATH', []);
             });
 
-            it('should report connection problems via event', function () {
+            it('should pass on connection problems', function () {
                 open.restore();
                 open = sinon.stub(Websock.prototype, 'open');
-                open.throws(Error('Failure'));
-                const client = new RFB(document.createElement('div'), 'ws://HOST:8675/PATH');
-                let callback = sinon.spy();
-                client.addEventListener('disconnect', callback);
-                this.clock.tick();
-                expect(callback).to.have.been.calledOnce;
-                expect(callback.args[0][0].detail.clean).to.be.false;
+                open.throws(new Error('Failure'));
+                expect(() => new RFB(document.createElement('div'), 'ws://HOST:8675/PATH')).to.throw('Failure');
             });
 
             it('should handle WebSocket/RTCDataChannel objects', function () {
                 let sock = new FakeWebSocket('ws://HOST:8675/PATH', []);
                 new RFB(document.createElement('div'), sock);
-                this.clock.tick();
                 expect(open).to.not.have.been.called;
                 expect(attach).to.have.been.calledOnceWithExactly(sock);
             });
@@ -189,7 +176,6 @@ describe('Remote Frame Buffer Protocol Client', function () {
                 const client = new RFB(document.createElement('div'), sock);
                 let callback = sinon.spy();
                 client.addEventListener('disconnect', callback);
-                this.clock.tick();
                 expect(open).to.not.have.been.called;
                 expect(attach).to.have.been.calledOnceWithExactly(sock);
                 // Check if it is ready for some data
@@ -200,25 +186,15 @@ describe('Remote Frame Buffer Protocol Client', function () {
             it('should refuse closed WebSocket/RTCDataChannel objects', function () {
                 let sock = new FakeWebSocket('ws://HOST:8675/PATH', []);
                 sock.readyState = WebSocket.CLOSED;
-                const client = new RFB(document.createElement('div'), sock);
-                let callback = sinon.spy();
-                client.addEventListener('disconnect', callback);
-                this.clock.tick();
-                expect(callback).to.have.been.calledOnce;
-                expect(callback.args[0][0].detail.clean).to.be.false;
+                expect(() => new RFB(document.createElement('div'), sock)).to.throw();
             });
 
-            it('should report attach problems via event', function () {
+            it('should pass on attach problems', function () {
                 attach.restore();
                 attach = sinon.stub(Websock.prototype, 'attach');
-                attach.throws(Error('Failure'));
+                attach.throws(new Error('Failure'));
                 let sock = new FakeWebSocket('ws://HOST:8675/PATH', []);
-                const client = new RFB(document.createElement('div'), sock);
-                let callback = sinon.spy();
-                client.addEventListener('disconnect', callback);
-                this.clock.tick();
-                expect(callback).to.have.been.calledOnce;
-                expect(callback.args[0][0].detail.clean).to.be.false;
+                expect(() => new RFB(document.createElement('div'), sock)).to.throw('Failure');
             });
         });