diff --git a/adafruit_minimqtt.py b/adafruit_minimqtt.py
index 5959dab6..ef7f3f6c 100644
--- a/adafruit_minimqtt.py
+++ b/adafruit_minimqtt.py
@@ -64,9 +64,8 @@
 MQTT_SUB = b'\x82'
 MQTT_UNSUB = b'\xA2'
 MQTT_PUB = bytearray(b'\x30\0')
-MQTT_CON = bytearray(b'\x10\0\0')
 # Variable CONNECT header [MQTT 3.1.2]
-MQTT_CON_HEADER = bytearray(b"\x04MQTT\x04\x02\0\0")
+MQTT_VAR_HEADER = bytearray(b"\x04MQTT\x04\x02\0\0")
 MQTT_DISCONNECT = b'\xe0\0'
 
 CONNACK_ERRORS = {const(0x01) : 'Connection Refused - Incorrect Protocol Version',
@@ -138,7 +137,7 @@ def __init__(self, socket, broker, port=None, username=None,
         self._is_connected = False
         self._msg_size_lim = MQTT_MSG_SZ_LIM
         self.packet_id = 0
-        self._keep_alive = 0
+        self._keep_alive = 60
         self._pid = 0
         self._user_data = None
         self._subscribed_topics = []
@@ -238,31 +237,53 @@ def connect(self, clean_session=True):
                 self._sock.connect(addr, TCP_MODE)
             except RuntimeError as e:
                 raise MMQTTException("Invalid broker address defined.", e)
-        premsg = MQTT_CON
-        msg = MQTT_CON_HEADER
-        msg[6] = clean_session << 1
-        sz = 12 + len(self._client_id)
+
+        # Fixed Header
+        fixed_header = bytearray()
+        fixed_header.append(0x10)
+
+        # Variable Header
+        var_header = MQTT_VAR_HEADER
+        var_header[6] = clean_session << 1
+
+        # Set up variable header and remaining_length
+        remaining_length = 12 + len(self._client_id)
         if self._user is not None:
-            sz += 2 + len(self._user) + 2 + len(self._pass)
-            msg[6] |= 0xC0
+            remaining_length += 2 + len(self._user) + 2 + len(self._pass)
+            var_header[6] |= 0xC0
         if self._keep_alive:
             assert self._keep_alive < MQTT_TOPIC_LENGTH_LIMIT
-            msg[7] |= self._keep_alive >> 8
-            msg[8] |= self._keep_alive & 0x00FF
+            var_header[7] |= self._keep_alive >> 8
+            var_header[8] |= self._keep_alive & 0x00FF
         if self._lw_topic:
-            sz += 2 + len(self._lw_topic) + 2 + len(self._lw_msg)
-            msg[6] |= 0x4 | (self._lw_qos & 0x1) << 3 | (self._lw_qos & 0x2) << 3
-            msg[6] |= self._lw_retain << 5
-        i = 1
-        while sz > 0x7f:
-            premsg[i] = (sz & 0x7f) | 0x80
-            sz >>= 7
-            i += 1
-        premsg[i] = sz
+            remaining_length += 2 + len(self._lw_topic) + 2 + len(self._lw_msg)
+            var_header[6] |= 0x4 | (self._lw_qos & 0x1) << 3 | (self._lw_qos & 0x2) << 3
+            var_header[6] |= self._lw_retain << 5
+
+        # Remaining length calculation
+        large_rel_length = False
+        if remaining_length > 0x7f:
+            large_rel_length = True
+            # Calculate Remaining Length [2.2.3]
+            while remaining_length > 0:
+                encoded_byte = remaining_length % 0x80
+                remaining_length = remaining_length // 0x80
+                # if there is more data to encode, set the top bit of the byte
+                if remaining_length > 0:
+                    encoded_byte |= 0x80
+                fixed_header.append(encoded_byte)
+        if large_rel_length:
+            fixed_header.append(0x00)
+        else:
+            fixed_header.append(remaining_length)
+            fixed_header.append(0x00)
+
         if self._logger is not None:
-            self._logger.debug('Sending CONNECT packet to broker')
-        self._sock.write(premsg)
-        self._sock.write(msg)
+            self._logger.debug('Sending CONNECT to broker')
+            self._logger.debug('Fixed Header: {}\nVariable Header: {}'.format(fixed_header,
+                                                                              var_header))
+        self._sock.write(fixed_header)
+        self._sock.write(var_header)
         # [MQTT-3.1.3-4]
         self._send_str(self._client_id)
         if self._lw_topic: