You should be using flooring screws. Yes there is such a thing. Even the big box stores will have them. If you sub-floor is 5/8" thick, the screw should have 5/8" of unthreaded stem undet the head. That will allow the screw to pull the sub-floor down tight. If the screw is fully threaded, if you start the screw with 1/8" gap between the subfloor and the joist, the screw will get tight when the head hits the top of the subfloor, but you can still have the 1/8" gap. Normally, with any screw, there will be some unthreaded stem under the screwhead, so the grip into the joist will be stronger, and if you torque the screw enough, you will pull the floorboard down tight, but just the same, its best to have the unthreaded stem on the screw as long as the thickness of your board.