Just want to point out something:

If the pedal is quiet when run off a battery but noisy with an adapter power source, then the noise has to be coming from the adapter. That's not to say that the pedal might not have a problem that's making it very sensitive to external noise sources, but it can't be amplifying noise that isn't there. Many less expensive power supplies tend to have some high frequency noise that can be picked up and amplified in a "gain pedal" like an overdrive, fuzz or distortion. So if the pedals that have worked well with a given P/S are of the "unity-gain" variety (modulation effects, envelope filters, delays, etc.), it's not surprising that the P/S might generate some noticeable noise when used with a gain circuit that amplifies incoming noise sources. But if you've used the P/S with other gain circuits and not had a problem, then I'd suspect that the pedal itself is excessively sensitive to noise for some reason, and should be replaced.