diff --git a/client.go b/client.go
index 106da2a..434f138 100644
--- a/client.go
+++ b/client.go
@@ -105,10 +105,10 @@ type Client struct {
 
 	mu sync.Mutex
 
-	closeChan         chan bool
-	messagesDone      chan bool
-	messageChan       chan *bytes.Buffer
-	messageProcessing uint32
+	closeChan    chan struct{}
+	closeOnce    sync.Once
+	messagesDone chan struct{}
+	messageChan  chan *bytes.Buffer
 
 	OnLookupCountry   func(*Client) string
 	OnClosed          func(*Client)
@@ -127,31 +127,23 @@ func NewClient(conn *websocket.Conn, remoteAddress string, agent string) (*Clien
 	}
 
 	client := &Client{
-		conn:   conn,
-		addr:   remoteAddress,
 		agent:  agent,
 		logRTT: true,
-
-		closeChan:    make(chan bool, 1),
-		messageChan:  make(chan *bytes.Buffer, 16),
-		messagesDone: make(chan bool, 1),
-
-		OnLookupCountry:   func(client *Client) string { return unknownCountry },
-		OnClosed:          func(client *Client) {},
-		OnMessageReceived: func(client *Client, data []byte) {},
-		OnRTTReceived:     func(client *Client, rtt time.Duration) {},
 	}
+	client.SetConn(conn, remoteAddress)
 	return client, nil
 }
 
 func (c *Client) SetConn(conn *websocket.Conn, remoteAddress string) {
 	c.conn = conn
 	c.addr = remoteAddress
-	c.closeChan = make(chan bool, 1)
+	c.closeChan = make(chan struct{})
 	c.messageChan = make(chan *bytes.Buffer, 16)
+	c.messagesDone = make(chan struct{})
 	c.OnLookupCountry = func(client *Client) string { return unknownCountry }
 	c.OnClosed = func(client *Client) {}
 	c.OnMessageReceived = func(client *Client, data []byte) {}
+	c.OnRTTReceived = func(c *Client, d time.Duration) {}
 }
 
 func (c *Client) IsConnected() bool {
@@ -188,38 +180,36 @@ func (c *Client) Country() string {
 }
 
 func (c *Client) Close() {
-	if !atomic.CompareAndSwapUint32(&c.closed, 0, 1) {
+	if atomic.LoadUint32(&c.closed) >= 2 {
+		// Prevent reentrant call in case this was the second closing
+		// step. Would otherwise deadlock in the "Once.Do" call path
+		// through "Hub.processUnregister" (which calls "Close" again).
 		return
 	}
 
-	c.mu.Lock()
-	if c.conn != nil {
-		c.conn.WriteMessage(websocket.CloseMessage, websocket.FormatCloseMessage(websocket.CloseNormalClosure, "")) // nolint
-	}
-	c.mu.Unlock()
-
-	if atomic.LoadUint32(&c.messageProcessing) == 1 {
-		// Defer closing
-		atomic.StoreUint32(&c.closed, 2)
-		return
-	}
-
-	c.doClose()
+	c.closeOnce.Do(func() {
+		c.doClose()
+	})
 }
 
 func (c *Client) doClose() {
-	c.closeChan <- true
-	<-c.messagesDone
+	closed := atomic.AddUint32(&c.closed, 1)
+	if closed == 1 {
+		c.mu.Lock()
+		defer c.mu.Unlock()
+		if c.conn != nil {
+			c.conn.WriteMessage(websocket.CloseMessage, websocket.FormatCloseMessage(websocket.CloseNormalClosure, "")) // nolint
+			c.conn.Close()
+			c.conn = nil
+		}
+	} else if closed == 2 {
+		// Both the read pump and message processing must be finished before closing.
+		close(c.closeChan)
+		<-c.messagesDone
 
-	c.OnClosed(c)
-	c.SetSession(nil)
-
-	c.mu.Lock()
-	if c.conn != nil {
-		c.conn.Close()
-		c.conn = nil
+		c.OnClosed(c)
+		c.SetSession(nil)
 	}
-	c.mu.Unlock()
 }
 
 func (c *Client) SendError(e *Error) bool {
@@ -341,7 +331,6 @@ func (c *Client) ReadPump() {
 }
 
 func (c *Client) processMessages() {
-	atomic.StoreUint32(&c.messageProcessing, 1)
 	for {
 		buffer := <-c.messageChan
 		if buffer == nil {
@@ -351,12 +340,9 @@ func (c *Client) processMessages() {
 		c.OnMessageReceived(c, buffer.Bytes())
 		bufferPool.Put(buffer)
 	}
-	atomic.StoreUint32(&c.messageProcessing, 0)
 
-	c.messagesDone <- true
-	if atomic.LoadUint32(&c.closed) == 2 {
-		c.doClose()
-	}
+	close(c.messagesDone)
+	c.doClose()
 }
 
 func (c *Client) writeInternal(message json.Marshaler) bool {