We report 292 hr of high speed photometry of the low amplitude ZZ Ceti star L19-2*. An adaptation of the method of power spectra of unequally-spaced data was devised to allow an efficient search for periodicities in the 105 000 data points.Five coherent oscillations were found, near 350, 192, 143, 118 and 113 s periods; each of these has multiple components, the largest in each case have amplitudes of 1.0, 6.0, 0.55, 1.8 and 2.2 x 103 mag respectively. The 192s oscillation in our observations possesses three components equally separated in frequency. When combined with earlier observations, however, we find evidence for a small departure from equality, by an amount in accordance with recent calculations of the second-order rotational splitting of g-mode oscillations in white dwarfs. No period changes were detected over a 4½ yr baseline. This establishes L19-2 as another very stable pulsating white dwarf. ©Royal Astronomical Society.