We have acquired 190 hours of high-speed photometry of the cataclysmic variable which is the probable optical counterpart of the hard X-ray source H 0551-819. An optical modulation at P = 2.9518 hr was always present, and probably represents the underlying orbital period of the binary. In 1995 January, no other period was obvious, but there was evidence for a signal of low coherence at P=2.88 hr. During the interval 1993 December-1994 February, the star displayed a much richer spectrum of periodic behavior, Aside from the orbital signal, there were also strong signals at P=3.053 and 1.500 hr, and a signal at 3.7 d. The two photometric signals at periods near but discrepant from P-orb suggest two kinds of ''superhumps'' in the star, possibly arising from apsidal and nodal precession of the accretion disk. Finally, the power spectrum at high frequency revealed oscillations with a period in the range 17-22 min; close study of the peaks showed evidence for underlying stable signals at P=1040.4, 1293.4, and 1707.6 s. These probably arise from the rapid rotation of the accreting white dwarf, with sidebands produced by reflection effects in the binary, The likely white-dwarf spin period is either 1040.4 or 2080.8 s.