My DD9 has a relatively low PSI and WM, and she sailed through the CogAT with no problem.

Kai, my district has historically used the CogAT and only the CogAT, even if you have WISC or other scores in hand. They claim that it measures a combination of IQ and achievement, and that students need to have both to qualify for the rigors of their program. But they won't let you substitute WISC+WJ, for example. It's really weird. The criteria have changed recently, and I think they are letting students in through other types of testing, but I don't know much about it.