We conducted time-resolved optical spectroscopy and/or time-series photometry of 15 cataclysmic binaries that were discovered in hard X-ray surveys by the Swift Burst Alert Telescope ( BAT ) and the International Gamma-Ray Astrophysics Laboratory ( INTEGRAL ) , with the goal of measuring their orbital periods and searching for spin periods . Four of the objects in this study are new optical identifications : Swift J0535.2+2830 , Swift J2006.4+3645 , IGR J21095+4322 , and Swift J2116.5+5336 . Coherent pulsations are detected from three objects for the first time , Swift J0535.2+2830 ( 1523 s ) , 2PBC J1911.4+1412 ( 747 s ) , and 1SWXRT J230642.7+550817 ( 464 s ) , indicating that they are intermediate polars ( IPs ) . We find two new eclipsing systems in time-series photometry : 2PBC J0658.0 - 1746 , a polar with a period of 2.38 hr , and Swift J2116.5+5336 , a disk system that has an eclipse period of 6.56 hr . Exact or approximate spectroscopic orbital periods are found for six additional targets . Of note is the long 4.637 day orbit for Swift J0623.9 - 0939 , which is revealed by the radial velocities of the photospheric absorption lines of the secondary star . We also discover a 12.76 hr orbital period for RX J2015.6+3711 , which confirms that the previously detected 2.00 hr X-ray period from this star is the spin period of an IP , as inferred by Coti Zelati et al . These results support the conclusion that hard X-ray selection favors magnetic CVs , with IPs outnumbering polars .