We solve the lifting problem in C^*-algebras for many sets of relations that
include the relations x_j^{N_j} = 0 on each variable. The remaining relations
must be of the form \| p(x_1,...,x_n) \| \leq C for C a positive constant and p
a noncommutative *-polynomial that is in some sense homogeneous. For example,
we prove liftability for the set of relations x^3=0, y^4=0, z^5=0,
xx^*+yy^*+zz^* \leq 1. Thus we find more noncommutative semialgebraic sets that
have the topology of noncommutative absolute retracts.