While highly evolved cataclysmic variables ( CVs ) with brown dwarf donors , often called ‘ ‘ period bouncers ’ ’ , are predicted to make up \simeq 40 - 70 % of the Galactic CV population , only a handful of such systems are currently known . The identification and characterization of additional period bouncers is therefore important to probe this poorly understood phase of CV evolution . We investigate the evolution of the CV QZ Lib following its 2004 super–outburst using multi–epoch spectroscopy . From time–resolved spectroscopic observations we measure the orbital period of the system , P _ { \mathrm { orb } } = 0.06436 ( 20 ) d , which , combined with the superhump period P _ { \mathrm { SH } } = 0.064602 ( 24 ) d , yields the system mass ratio , q = 0.040 ( 9 ) . From the analysis of the spectral energy distribution we determine the structure of the accretion disc and the white dwarf effective temperature , T _ { \mathrm { eff } } = 10 500 \pm 1500 \mathrm { K } . We also derive an upper limit on the effective temperature of the secondary , T _ { \mathrm { eff } } \lesssim 1700 \mathrm { K } , corresponding to a brown dwarf of T spectral type . The low temperature of the white dwarf , the small mass ratio and the fact that the donor is not dominating the near–infrared emission are all clues of a post bounce system . Although it is possible that QZ Lib could have formed as a white dwarf plus a brown dwarf binary , binary population synthesis studies clearly suggest this scenario to be less likely than a period bouncer detection and we conclude that QZ Lib is a CV that has already evolved through the period minimum .