  We propose a new approach, based on the puncture method, to construct black
hole initial data in the so-called trumpet geometry, i.e. on slices that
asymptote to a limiting surface of non-zero areal radius. Our approach is easy
to implement numerically and, at least for non-spinning black holes, does not
require any internal boundary conditions. We present numerical results,
obtained with a uniform-grid finite-difference code, for boosted black holes
and binary black holes. We also comment on generalizations of this method for
spinning black holes.
