We have detected 21 new, very hot hydrogen-deficient (pre-) white dwarfs (spectral types O(He), hot DO, PG1159) in the Data Release 10 of the Sloan Digital Sky Survey. We present the results of non-local thermodynamic equilibrium (non-LTE) model-atmosphere analyses. The seven PG1159 stars have effective temperatures and surface gravities in the ranges T eff = 100 000-140 000 K and log g = 6-7.5. The hottest one is a new member of the rare hybrid-PG1159 subtype, indicating the presence of residual hydrogen. The ten new hot DOs span T eff = 65 000-120 000 K and log g = 7.5-8. Carbon abundances were derived and it is found that the PG1159 star values (C/He = 0.33-0.03 by number) and the DO values (<0.0004-0.01) cover distinct but adjacent ranges. With the discovery of four new O(He) stars (T eff = 80 000-100 000 K, log g = 5-5.5, C/He = 0.002-0.01), we double the number of known members of this rare spectral class. One of them is particularly interesting because it is unusually rich in C, N, O, and Si. Unexpected problems arose with the DOs because many He ii lines of every other star are so deep that they cannot be matched by any model. This is most conspicuous in the case of one object which exhibits the occurrence of ultrahigh-ionization metal features, a hitherto unexplained phenomenon that is known from a disquieting large fraction of hot DOs.