We study the formation and evolution of DA white dwarfs, the progenitors of which have experienced a late thermal pulse (LTP) shortly after the departure from the thermally pulsing AGB. To this end, we compute the complete evolution of an initially 2.7 M⊙ star all the way from the zero-age main sequence to the white dwarf stage. We find that most of the original H-rich material of the post-AGB remnant is burnt during the post-LTP evolution, with the result that, at entering its white dwarf cooling track, the remaining H envelope becomes 10-6 M⊙ in agreement with asteroseismological inferences for some ZZ Ceti stars.