diff --git a/ChangeLog.txt b/ChangeLog.txt
index 6601a1d29f..a5fd7eb67d 100644
--- a/ChangeLog.txt
+++ b/ChangeLog.txt
@@ -20,10 +20,15 @@ Client library:
 - `mosquitto_string_option(mosq, MOSQ_OPT_TLS_KEYFORM, ...)` was incorrectly
   returning `MOSQ_ERR_INVAL` with valid input. This has been fixed.
   Closes #1360.
+- on_connect callback is now called with the correct v5 reason code if a v5
+  client connects to a v3.x broker and is sent a CONNACK with the
+  "unacceptable protocol version" connack reason code.
 
 Clients:
 - mosquitto_pub: fix error codes not being returned when mosquitto_pub exits.
   Closes #1354.
+- All clients: improve error messages when connecting to a v3.x broker when in
+  v5 mode. Closes #1344.
 
 Other:
 - Various documentation fixes.
diff --git a/client/pub_client.c b/client/pub_client.c
index 69cea64216..0debcaee39 100644
--- a/client/pub_client.c
+++ b/client/pub_client.c
@@ -168,10 +168,15 @@ void my_connect_callback(struct mosquitto *mosq, void *obj, int result, int flag
 	}else{
 		if(result){
 			if(cfg.protocol_version == MQTT_PROTOCOL_V5){
-				err_printf(&cfg, "%s\n", mosquitto_reason_string(result));
+				if(result == MQTT_RC_UNSUPPORTED_PROTOCOL_VERSION){
+					err_printf(&cfg, "Connection error: %s. Try connecting to an MQTT v5 broker, or use MQTT v3.x mode.\n", mosquitto_reason_string(result));
+				}else{
+					err_printf(&cfg, "Connection error: %s\n", mosquitto_reason_string(result));
+				}
 			}else{
-				err_printf(&cfg, "%s\n", mosquitto_connack_string(result));
+				err_printf(&cfg, "Connection error: %s\n", mosquitto_connack_string(result));
 			}
+			mosquitto_disconnect_v5(mosq, 0, cfg.disconnect_props);
 		}
 	}
 }
diff --git a/client/rr_client.c b/client/rr_client.c
index 02801e829a..44f105b02f 100644
--- a/client/rr_client.c
+++ b/client/rr_client.c
@@ -122,7 +122,11 @@ void my_connect_callback(struct mosquitto *mosq, void *obj, int result, int flag
 	}else{
 		client_state = rr_s_disconnect;
 		if(result){
-			err_printf(&cfg, "%s\n", mosquitto_connack_string(result));
+			if(result == MQTT_RC_UNSUPPORTED_PROTOCOL_VERSION){
+				err_printf(&cfg, "Connection error: %s. mosquitto_rr only supports connecting to an MQTT v5 broker\n", mosquitto_reason_string(result));
+			}else{
+				err_printf(&cfg, "Connection error: %s\n", mosquitto_reason_string(result));
+			}
 		}
 		mosquitto_disconnect_v5(mosq, 0, cfg.disconnect_props);
 	}
@@ -356,7 +360,7 @@ int main(int argc, char *argv[])
 	}
 	client_config_cleanup(&cfg);
 	if(rc){
-		fprintf(stderr, "Error: %s\n", mosquitto_strerror(rc));
+		err_printf(&cfg, "Error: %s\n", mosquitto_strerror(rc));
 	}
 	return rc;
 
diff --git a/client/sub_client.c b/client/sub_client.c
index a279b2491c..68b0e79084 100644
--- a/client/sub_client.c
+++ b/client/sub_client.c
@@ -126,9 +126,13 @@ void my_connect_callback(struct mosquitto *mosq, void *obj, int result, int flag
 	}else{
 		if(result){
 			if(cfg.protocol_version == MQTT_PROTOCOL_V5){
-				err_printf(&cfg, "%s\n", mosquitto_reason_string(result));
+				if(result == MQTT_RC_UNSUPPORTED_PROTOCOL_VERSION){
+					err_printf(&cfg, "Connection error: %s. Try connecting to an MQTT v5 broker, or use MQTT v3.x mode.\n", mosquitto_reason_string(result));
+				}else{
+					err_printf(&cfg, "Connection error: %s\n", mosquitto_reason_string(result));
+				}
 			}else{
-				err_printf(&cfg, "%s\n", mosquitto_connack_string(result));
+				err_printf(&cfg, "Connection error: %s\n", mosquitto_connack_string(result));
 			}
 		}
 		mosquitto_disconnect_v5(mosq, 0, cfg.disconnect_props);
@@ -353,7 +357,7 @@ int main(int argc, char *argv[])
 	}
 	client_config_cleanup(&cfg);
 	if(rc){
-		fprintf(stderr, "Error: %s\n", mosquitto_strerror(rc));
+		err_printf(&cfg, "Error: %s\n", mosquitto_strerror(rc));
 	}
 	return rc;
 
diff --git a/lib/handle_connack.c b/lib/handle_connack.c
index 19b6a66160..60780f6ca1 100644
--- a/lib/handle_connack.c
+++ b/lib/handle_connack.c
@@ -28,6 +28,29 @@ and the Eclipse Distribution License is available at
 #include "property_mosq.h"
 #include "read_handle.h"
 
+static void connack_callback(struct mosquitto *mosq, uint8_t reason_code, uint8_t connect_flags, const mosquitto_property *properties)
+{
+	log__printf(mosq, MOSQ_LOG_DEBUG, "Client %s received CONNACK (%d)", mosq->id, reason_code);
+	pthread_mutex_lock(&mosq->callback_mutex);
+	if(mosq->on_connect){
+		mosq->in_callback = true;
+		mosq->on_connect(mosq, mosq->userdata, reason_code);
+		mosq->in_callback = false;
+	}
+	if(mosq->on_connect_with_flags){
+		mosq->in_callback = true;
+		mosq->on_connect_with_flags(mosq, mosq->userdata, reason_code, connect_flags);
+		mosq->in_callback = false;
+	}
+	if(mosq->on_connect_v5){
+		mosq->in_callback = true;
+		mosq->on_connect_v5(mosq, mosq->userdata, reason_code, connect_flags, properties);
+		mosq->in_callback = false;
+	}
+	pthread_mutex_unlock(&mosq->callback_mutex);
+}
+
+
 int handle__connack(struct mosquitto *mosq)
 {
 	uint8_t connect_flags;
@@ -44,7 +67,17 @@ int handle__connack(struct mosquitto *mosq)
 
 	if(mosq->protocol == mosq_p_mqtt5){
 		rc = property__read_all(CMD_CONNACK, &mosq->in_packet, &properties);
-		if(rc) return rc;
+
+		if(rc == MOSQ_ERR_PROTOCOL && reason_code == CONNACK_REFUSED_PROTOCOL_VERSION){
+			/* This could occur because we are connecting to a v3.x broker and
+			 * it has replied with "unacceptable protocol version", but with a
+			 * v3 CONNACK. */
+
+			connack_callback(mosq, MQTT_RC_UNSUPPORTED_PROTOCOL_VERSION, connect_flags, NULL);
+			return rc;
+		}else if(rc){
+			return rc;
+		}
 	}
 
 	mosquitto_property_read_string(properties, MQTT_PROP_ASSIGNED_CLIENT_IDENTIFIER, &clientid, false);
@@ -68,24 +101,7 @@ int handle__connack(struct mosquitto *mosq)
 
 	mosq->msgs_out.inflight_quota = mosq->msgs_out.inflight_maximum;
 
-	log__printf(mosq, MOSQ_LOG_DEBUG, "Client %s received CONNACK (%d)", mosq->id, reason_code);
-	pthread_mutex_lock(&mosq->callback_mutex);
-	if(mosq->on_connect){
-		mosq->in_callback = true;
-		mosq->on_connect(mosq, mosq->userdata, reason_code);
-		mosq->in_callback = false;
-	}
-	if(mosq->on_connect_with_flags){
-		mosq->in_callback = true;
-		mosq->on_connect_with_flags(mosq, mosq->userdata, reason_code, connect_flags);
-		mosq->in_callback = false;
-	}
-	if(mosq->on_connect_v5){
-		mosq->in_callback = true;
-		mosq->on_connect_v5(mosq, mosq->userdata, reason_code, connect_flags, properties);
-		mosq->in_callback = false;
-	}
-	pthread_mutex_unlock(&mosq->callback_mutex);
+	connack_callback(mosq, reason_code, connect_flags, properties);
 	mosquitto_property_free_all(&properties);
 
 	switch(reason_code){
diff --git a/lib/loop.c b/lib/loop.c
index 2342c945aa..36763e06c3 100644
--- a/lib/loop.c
+++ b/lib/loop.c
@@ -314,7 +314,6 @@ static int mosquitto__loop_rc_handle(struct mosquitto *mosq, int rc)
 			mosq->in_callback = false;
 		}
 		pthread_mutex_unlock(&mosq->callback_mutex);
-		return rc;
 	}
 	return rc;
 }