I don't understand how installing a smaller pulley could make the car run too rich (unless I have the terminology reversed). The purpose of a SuperCharger is to increase air pressure and density in the intake manifold (we used to call them blowers in the old days

). Putting a smaller pulley on, creating more pressure should force more air and make the car run leaner. I thought lean/rich referred to the amount of fuel in the air/fuel mixture. Lean being too little fuel and rich being too much fuel.
Then the problem would be that since you are increasing the volume of air, there is the potential that your fuel injectors were not able to supply the volume of fuel to allow for the correct mixture or possibly that the injectors were ok but the fuel pump could not supply the volume to the injectors. The computer calibrated for stock will be telling the fuel system it needs less fuel than we require with superchargers running smaller pulleys so we use the APEXi S-AFCii to recalibrate the mixture.
Should be as simple as this; you put a smaller pulley on and S-AFC, try to dyno tune the car to give the propper air/fuel mixture. If you can't get enough fuel to allow the correct mixture, you need to upgrade the injectors and/or the fuel pump. Guessing the injectors should be the first choice and if they still can't provide enough fuel, then the fuel pump.
I could have this all screwed up, I'm still learning. Anyone that really knows validate or correct. Has anyone done this testing with a 6psi pulley installed? I've heard some say stock fuel pump and injectors with 6psi and S-AFC dyno tuned worked fine. Then others say they couldn't get the correct air/fuel mixture. HELP??? -JoeB