Instead of using Rabbit Ears, which are VERY tempermental, even with the best of signals, why not get something like the Silver Sensor (a directional indoor antenna). It will be far less susceptible to you moving about the room and other reflections, because of its directionality. You can find one for 20 some bucks.
Another alternative:
Radio Shack makes a model U-71 UHF/Corner Reflector that is 40" long...a very good, yet small UHF antenna. You might find a place you can tuck it away and it will outperform rabbit hears by at least an order of magnitude (X 10). Of course, all of this assumes all your TV stations are coming from the same direction....if not, then you'll have to point either the Silver Sensor or the U-71 at your various sources.
We're lucky here...all the transmitters/antennas are at the same location.