  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.
