I somehow stumbled acrosshttp://www.voip-info.org/wiki/view/Asterisk+tips+SIP+URI+Dial
It has the solution. Don't know why I didn't see it before or exactly how I found it this time :).
One thing that I didn't really get from the sip.conf page was how definitions in the [authentication] section relate to user registrations and to incoming calls. But they do...