don't just use the adjuster. that's for fine-tuning. unhook your anchor bolt (the bolt that clamps the cable to the caliper) so that the cable is loose. pull on the cable and give it a good amount of tension while adjusting the caliper to your desired rim clearance (this is very easy to do with a fourth-hand tool available at your LBS, or get a buddy to help you). with the cable still tense, re-secure the anchor bolt and there you go.

park tool's website has a nice guide on brake caliper adjustment.