  Let M be a hyperbolic n-manifold whose cusps have torus cross-sections. In
arXiv:0901.0056, the authors constructed a variety of nonpositively and
negatively curved spaces as "2\pi-fillings" of M by replacing the cusps of M
with compact "partial cones" of their boundaries. These 2\pi-fillings are
closed pseudomanifolds, and so have a fundamental class. We show that the
simplicial volume of any such 2\pi-filling is positive, and bounded above by
Vol(M)/v_n, where v_n is the volume of a regular ideal hyperbolic n-simplex.
This result generalizes the fact that hyperbolic Dehn filling of a 3-manifold
does not increase hyperbolic volume.
  In particular, we obtain information about the simplicial volumes of some
4--dimensional homology spheres described by Ratcliffe and Tschantz, answering
a question of Belegradek and establishing the existence of 4--dimensional
homology spheres with positive simplicial volume.
