Aims.The present paper focuses on the evolution of hydrogen-deficient white dwarfs with the aim of exploring the consequences of different initial envelope structures on the carbon abundances expected in helium-rich, carbon-contaminated DQ white dwarfs. In particular, the evolutionary link between the DQs with low detected carbon abundances and the PG 1159, extreme horizontal branch, and helium-rich R Coronae Borealis (RCrB) stars is explored. Methods: .We present full evolutionary calculations that take a self-consistent treatment of element diffusion into account as well as expectations for the outer layer chemical stratification of progenitor stars upon entering the white dwarf regime. Results: .We find that PG 1159 stars cannot be related to any DQ white dwarfs with low C abundances. Instead, we suggest that the latter could constitute the progeny of the giant, helium-rich RCrB stars.