After quite some time, I discovered the problem to be /var/spool/exim4/gnutls-params.
On my systems that hadn't been running exim4 before, but had freshly installed this version, it was a happy ASCII text file. On the system with the problem, it had binary data in it. On a whim, I ran /usr/share/exim4/exim4_refresh_gnutls-params, which solved the problem. No idea why it was a problem, or why this fixed it. -- To UNSUBSCRIBE, email to [EMAIL PROTECTED] with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]