We report detailed follow-up observations of the cataclysmic variable HS 2331+3905 , identified as an emission-line object in the Hamburg Quasar Survey . An orbital period of 81.08 min is unambiguously determined from the detection of eclipses in the light curves of HS 2331+3905 . A second photometric period is consistently detected at P \simeq 83.38 min , \sim 2.8 \% longer than P _ { orb } , which we tentatively relate to the presence of permanent superhumps . High time resolution photometry exhibits short-timescale variability on time scales of \simeq 5 - 6 min which we interpret as non-radial white dwarf pulsations , as well as a coherent signal at 1.12 min , which is likely to be the white dwarf spin period . A large-amplitude quasi-sinusoidal radial velocity modulation of the Balmer and Helium lines with a period \sim 3.5 h is persistently detected throughout three seasons of time-resolved spectroscopy . However , this spectroscopic period , which is in no way related to the orbital period , is not strictly coherent but drifts in period and/or phase on time scales of a few days . Modeling the far-ultraviolet to infrared spectral energy distribution of HS 2331+3905 , we determine a white dwarf temperature of \mbox { $T _ { \mathrm { eff } } $ } \simeq 10 500 K ( assuming M _ { wd } = 0.6 M _ { \odot } ) , close to the ZZ Ceti instability strip of single white dwarfs . The spectral model implies a distance of d = 90 \pm 15 pc , and a low value for the distance is supported by the large proper motion of the system , \mu = 0.14 \arcsec \mathrm { yr ^ { -1 } } . The non-detection of molecular bands and the low J , H , and K fluxes of HS 2331+3905 make this object a very likely candidate for a brown-dwarf donor .