I noticed air conditioners blow the coldest air when the fan speed is on low and kept on low. I experimented with my brothers air conditioner and it kept his place real cool considering his apartment faced the warmest side of the building and he was on the 3rd floor.
Try this for yourself. Keep the fan speed on low and simply adjust the thermostat. It really does work. And when it cools down enough, the compressor turns off / on - actually saving electricity.