Resolving in LX zones

After creating an LX zone, I notice that resolvconf contains a few DNS servers I did not tell it to create, namely the Google servers (at 4.4.4.4 and 8.8.8.8) and a Joyent one at 216.52.1.1.

My own DNS server is added to /etc/resolvconf/resolv.conf.d/tail, but it never works (pinging a host in my local domain results in timeouts, for example).

The root for the resolvconf entries is /run/resolvconf/interface/original.resolvconf. If I delete the entries from that file, DNS works properly.