  The Vainshtein mechanism suppresses the fifth force at astrophysical
distances, while enabling it to compete with gravity at cosmological scales.
Typically, Vainshtein solutions exhibit superluminal perturbations. However, a
restricted class of solutions with special boundary conditions were shown to be
devoid of the faster-than-light modes. Here we extend this class by finding
solutions in a theory of quasidilaton, amended by derivative terms consistent
with its symmetries. Solutions with Minkowski asymptotics are not stable, while
the ones that exhibit the Vainshtein mechanism by transitioning to cosmological
backgrounds are free of ghosts, tachyons, gradient instability, and
superluminality, for all propagating modes present in the theory. These
solutions require special choice of the strength and signs of nonlinear terms,
as well as a choice of asymptotic cosmological boundary conditions.
