New designs of obtaining dual-band circular polarization (CP) radiation of a single-feed square microstrip antenna are proposed and experimentally studied. The proposed single-feed dual-band CP designs are achieved by inserting four T-shaped slits at the patch edges or four Y-shaped slits at the patch corners of a square microstrip antenna. From experiments conducted, a patch size reduction as large as 36% for the proposed design, compared to a conventional CP design without the inserted slits, has been obtained. Details of the design considerations of the proposed antennas are described, and experimental results of the obtained dual-band CP performances are presented and discussed.