Pickups can't really "compress" a signal,
per se, but they can be over-wound to the point that they overdrive the snot out of the amp's input stage, which causes the amp to compress the signal (at least in tube-based amps - solid state amps usually break up kinda ugly when overdriven). Downside is, it's usually so dirty and lacks so much high end that you lose a great deal of the musical quality of a stringed instrument. Of course, there are all points in between.
Active pickups have evolved over the years. They were originally a good way to get the "fatter" sound of a PAF-style pup with the clarity of a single coil, but not generate any noise. As a result, a lot of people were sorta disappointed. Looked like a wicked humbucker, but sounded kinda sterile/brittle (relatively speaking). They sound better now, but it's still a lotta trouble/cost to go through to eliminate noise while maintaining clarity and high output. There are a LOT of choices out there that will give you that without the electronics, fancy wiring, switches, batteries, etc.
You may want to just try a set of the popular noiseless pickups, and experiment with height adjustments. It's surprising what lowering the things will do for clarity.
The "Area" series from DiMarzio is popular, but they have a lot of others. I like
GFS' "True Coils" and "
Neovins". Bill Lawrence has some nice parts called "
Microcoils". Of course, there are the exotics like Kinmans and Lollars if you just can't figure out what to do with those pesky bags of money you keep tripping over. They all sound a
very much like regular single coils without the dreaded hum.