I'd noticed for years that sending outbound e-mail from Thunderbird to my server on port 587 took far longer than it should have - about six seconds of staring at the progress bar.

Today, I was finally bored enough to work out the cause: Exim is configured to perform ident checks, which take 5 seconds to time out. Since port 587 only accepts mail from authenticated users, we can disable the ident checks for it:

rfc1413_hosts = ${if eq{$interface_port}{25}{*}{! $sender_host_address}}

If you're running Debian, change the above in /etc/exim4/conf.d/main/02_exim4-config_options.