diff --git a/src/plumpy/exceptions.py b/src/plumpy/exceptions.py
index 6f0c75a4..1e6f3b26 100644
--- a/src/plumpy/exceptions.py
+++ b/src/plumpy/exceptions.py
@@ -38,3 +38,6 @@ class PersistenceError(Exception):
 
 class ClosedError(Exception):
     """Raised when an mutable operation is attempted on a closed process"""
+
+class TaskRejectedError(Exception):
+    """ A task was rejected by the coordinacor"""
diff --git a/src/plumpy/message.py b/src/plumpy/message.py
index b18d4123..024d008f 100644
--- a/src/plumpy/message.py
+++ b/src/plumpy/message.py
@@ -7,6 +7,8 @@
 
 import kiwipy
 
+from plumpy.exceptions import PersistenceError, TaskRejectedError
+
 from . import loaders, persistence
 from .utils import PID_TYPE
 
@@ -188,8 +190,6 @@ async def __call__(self, communicator: kiwipy.Communicator, task: Dict[str, Any]
         Receive a task.
         :param task: The task message
         """
-        from plumpy.rmq import communications
-
         task_type = task[TASK_KEY]
         if task_type == LAUNCH_TASK:
             return await self._launch(communicator, **task.get(TASK_ARGS, {}))
@@ -198,7 +198,7 @@ async def __call__(self, communicator: kiwipy.Communicator, task: Dict[str, Any]
         if task_type == CREATE_TASK:
             return await self._create(communicator, **task.get(TASK_ARGS, {}))
 
-        raise communications.TaskRejected
+        raise TaskRejectedError
 
     async def _launch(
         self,
@@ -220,10 +220,8 @@ async def _launch(
         :param init_kwargs: keyword arguments to the process constructor
         :return: the pid of the created process or the outputs (if nowait=False)
         """
-        from plumpy.rmq import communications
-
         if persist and not self._persister:
-            raise communications.TaskRejected('Cannot persist process, no persister')
+            raise PersistenceError('Cannot persist process, no persister')
 
         if init_args is None:
             init_args = ()
@@ -255,11 +253,9 @@ async def _continue(
         :param nowait: if True don't wait for the process to complete
         :param tag: the checkpoint tag to continue from
         """
-        from plumpy.rmq import communications
-
         if not self._persister:
             LOGGER.warning('rejecting task: cannot continue process<%d> because no persister is available', pid)
-            raise communications.TaskRejected('Cannot continue process, no persister')
+            raise PersistenceError('Cannot continue process, no persister')
 
         # Do not catch exceptions here, because if these operations fail, the continue task should except and bubble up
         saved_state = self._persister.load_checkpoint(pid, tag)
@@ -292,10 +288,8 @@ async def _create(
         :param init_kwargs: keyword arguments to the process constructor
         :return: the pid of the created process
         """
-        from plumpy.rmq import communications
-
         if persist and not self._persister:
-            raise communications.TaskRejected('Cannot persist process, no persister')
+            raise PersistenceError('Cannot persist process, no persister')
 
         if init_args is None:
             init_args = ()