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debugging TLS alert

I'm trying to use exim4 to send email to another site.  My host
connects, negotiates a TLS connection and sends what seems to be a
reasonable amount of application data.

I then get an encrypted alert from the other host, the connection shuts
down, and the email doesn't get delivered.  I don't get any errors in my
exim4 log.

To the best of my knowledge, the other site is the only one I try to
send email to that is having the problem, and mine is the only host
having trouble sending to that site.

So...  any words of wisdom on how to debug this?  I've trying turning
all logging on in exim4, and didn't get anything helpful.  Is there a
way to turn logging on in gnutls?