diff --git a/plumpy/processes.py b/plumpy/processes.py
index 783ac5f1..5dee8210 100644
--- a/plumpy/processes.py
+++ b/plumpy/processes.py
@@ -296,7 +296,7 @@ def init(self) -> None:
                 identifier = self._communicator.add_rpc_subscriber(self.message_receive, identifier=str(self.pid))
                 self.add_cleanup(functools.partial(self._communicator.remove_rpc_subscriber, identifier))
             except kiwipy.TimeoutError:
-                self.logger.exception('Process<%s> failed to register as an RPC subscriber', self.pid)
+                self.logger.exception('Process<%s>: failed to register as an RPC subscriber', self.pid)
 
             try:
                 identifier = self._communicator.add_broadcast_subscriber(
@@ -304,14 +304,14 @@ def init(self) -> None:
                 )
                 self.add_cleanup(functools.partial(self._communicator.remove_broadcast_subscriber, identifier))
             except kiwipy.TimeoutError:
-                self.logger.exception('Process<%s> failed to register as a broadcast subscriber', self.pid)
+                self.logger.exception('Process<%s>: failed to register as a broadcast subscriber', self.pid)
 
         if not self._future.done():
 
             def try_killing(future: futures.Future) -> None:
                 if future.cancelled():
                     if not self.kill('Killed by future being cancelled'):
-                        self.logger.warning('Failed to kill process on future cancel')
+                        self.logger.warning('Process<%s>: Failed to kill process on future cancel', self.pid)
 
             self._future.add_done_callback(try_killing)
 
@@ -690,12 +690,15 @@ def on_entered(self, from_state: Optional[process_states.State]) -> None:
         if self._communicator and isinstance(self.state, enum.Enum):
             from_label = cast(enum.Enum, from_state.LABEL).value if from_state is not None else None
             subject = 'state_changed.{}.{}'.format(from_label, self.state.value)
-            self.logger.info('Broadcasting state change of %d: %s', self.pid, subject)
+            self.logger.info('Process<%s>: Broadcasting state change: %s', self.pid, subject)
             try:
                 self._communicator.broadcast_send(body=None, sender=self.pid, subject=subject)
             except ConnectionClosed:
-                message = 'no connection available to broadcast state change from %s to %s'
-                self.logger.info(message, from_label, self.state.value)
+                message = 'Process<%s>: no connection available to broadcast state change from %s to %s'
+                self.logger.warning(message, self.pid, from_label, self.state.value)
+            except kiwipy.TimeoutError:
+                message = 'Process<%s>: sending broadcast of state change from %s to %s timed out'
+                self.logger.warning(message, self.pid, from_label, self.state.value)
 
     def on_exiting(self) -> None:
         state = self.state
@@ -842,7 +845,7 @@ def on_close(self) -> None:
                 try:
                     cleanup()
                 except Exception:  # pylint: disable=broad-except
-                    self.logger.exception('Exception calling cleanup method %s', cleanup)
+                    self.logger.exception('Process<%s>: Exception calling cleanup method %s', self.pid, cleanup)
             self._cleanups = None
         finally:
             self._event_callbacks = {}
@@ -863,7 +866,7 @@ def message_receive(self, _comm: kiwipy.Communicator, msg: Dict[str, Any]) -> An
         :param msg: the message
         :return: the outcome of processing the message, the return value will be sent back as a response to the sender
         """
-        self.logger.debug("RPC message '%s' received with communicator '%s'", msg, _comm)
+        self.logger.debug("Process<%s>: received RPC message with communicator '%s': %r", self.pid, _comm, msg)
 
         intent = msg[process_comms.INTENT_KEY]
 
@@ -890,7 +893,9 @@ def broadcast_receive(self, _comm: kiwipy.Communicator, body: Any, sender: Any,
         :param msg: the message
         """
         # pylint: disable=unused-argument
-        self.logger.debug("Broadcast message '%s' received with communicator '%s'", body, _comm)
+        self.logger.debug(
+            "Process<%s>: received broadcast message '%s' with communicator '%s': %r", self.pid, subject, _comm, body
+        )
 
         # If we get a message we recognise then action it, otherwise ignore
         if subject == process_comms.Intent.PLAY: