[exim] configuring exim4 smtp to use SSL

I'm running a Debian Wheezy/64 server and am trying to get exim4 to send
e-mail using an SSL connection. My current configuration works when I
use their normal smtp port (which is 26, not 25) but fails when I use
their smtp/SSL port (465).

However Thunderbird is able to send e-mail from workstations to the same
server using port 465 and have SSL/TLS identified as the connection
security.

My update-exim4.conf.conf file (which Debian uses to avoid
dpkg-reconfigure exim4) is (replacing <remote host name> with the actual
name). If dc_smarthost has the port set to 26, mail gets sent. However
with it set to 465, it stays in the mailq.

dc_eximconfig_configtype='smarthost'
dc_other_hostnames=''
dc_local_interfaces='127.0.0.1'
dc_readhost='<remote host name>'
dc_relay_domains=''
dc_minimaldns='false'
dc_relay_nets=''
dc_smarthost='<remote host name>:465'
CFILEMODE='644'
dc_use_split_config='false'
dc_hide_mailname='false'
dc_mailname_in_oh='true'
dc_localdelivery='mail_spool'

Any ideas?