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Context. White dwarfs are nowadays routinely used as reliable cosmochronometers, allowing several stellar populations to be dated. Aims. We present new white dwarf evolutionary sequences for low-metallicity progenitors. This is motivated by the recent finding that residual H burning in low-mass white dwarfs resulting from Z = 0.0001 progenitors is the main energy source over a significant part of their evolution. Methods. White dwarf sequences have been derived from full evolutionary calculations that take the entire history of progenitor stars into account, including the thermally pulsing and the post-asymptotic giant branch (AGB) phases. Results. We show that for progenitor metallicities in the range 0.00003 ≲ Z ≲ 0.001, and in the absence of carbon enrichment from the occurrence of a third dredge-up episode, the resulting H envelope of the low-mass white dwarfs is thick enough to make stable H burning the most important energy source even at low luminosities. This has a significant impact on white dwarf cooling times. This result is independent of the adopted mass-loss rate during the thermally-pulsing and post-AGB phases and in the planetary nebulae stage. Conclusions. We conclude that in the absence of third dredge-up episodes, a significant part of the evolution of low-mass white dwarfs resulting from low-metallicity progenitors is dominated by stable H burning. Our study opens the possibility of using the observed white dwarf luminosity function of low-metallicity globular clusters to constrain the efficiency of third dredge up episodes during the thermally-pulsing AGB phase of low-metallicity progenitors., Facultad de Ciencias Astronómicas y Geofísicas, Instituto de Astrofísica de La Plata