Upgrades fail with a message about "Old queue files present"

[Mark Shuttleworth]

The message says:

---BEGIN UPGRADE MESSAGE---
The directory /var/lib/mailman/qfiles contains files

The message says:

---BEGIN UPGRADE MESSAGE---
The directory /var/lib/mailman/qfiles contains files. It needs to be empty for the upgrade work properly. Please either flush the queue (by way of mailmanctl start, then stopping it and redoing the upgrade when it is finished) or remove those files. Note that removing the files will lose some emails sent to lists.
---END UPGRADE MESSAGE---

But nowhere does it tell you how to stop the flow of messages into mailman, so that the rogue messages can be dealt with without new ones creeping into the mix.