I believe I forgot to mention, I'm using 1.5-i386.

>I have successfully had my server configured with the following
>/etc/ifconfig.rtk0 file:
>inet 192.168.1.3 netmask 0xffffff00 media autoselect
>inet 192.168.1.2 netmask 0xffffff00 alias

I had added these in ifconfig.rtk0 instead of /etc/ifaliases, because this
is said in /etc/rc.d/network:

        # Note that /etc/ifaliases works only with certain cases only and its
        # use is not recommended.  Use /etc/ifconfig.xxN instead.

(I wonder why this isn't in the manpage for ifaliases, BTW.)

However, using /etc/ifaliases appears to do one thing that adding the alias
to ifconfig.xxN doesn't (again from /etc/rc.d/network, a bit later on):

                        # use loopback, not the wire
                        route add $addr 127.0.0.1

By adding this route manually, my problems were solved. Searching the list
archives turned up very little, but now I wonder whether I might be able to
solve this without adding the route, and setting an all-1 netmask for the
aliases? But now that things work as required, I am less inclined to
experiment.

Thanks to Brian de Alwis for helping me solve this.

-Lasse