  Recent work on holographic superconductivity and gravitational duals of
systems with non-relativistic conformal symmetry have made use of consistent
truncations of D=10 and D=11 supergravity retaining some massive modes in the
Kaluza-Klein tower. In this paper we focus on reductions of IIB supergravity to
five dimensions on a Sasaki-Einstein manifold, and extend these previous
truncations to encompass the entire bosonic sector of gauged D=5, N=2
supergravity coupled to massive multiplets up to the second Kaluza-Klein level.
We conjecture that a necessary condition for the consistency of massive
truncations is to only retain the lowest modes in the massive trajectories of
the Kaluza-Klein mode decomposition of the original fields. This is an
extension of the well-known result that consistent truncations may be obtained
by restricting to the singlet sector of the internal symmetry group.
