  We revisit the construction of puncture black hole initial data in the
conformal thin-sandwich decomposition of Einstein's constraint equations. It
has been shown previously that this approach cannot yield quasiequilibrium
wormhole data, which connect two asymptotically flat spatial infinities. This
argument does not apply to trumpet data, which connect the spatial infinity in
one universe with the future timelike infinity of another. As a numerical
demonstration we present results for a single boosted trumpet-puncture black
holes, constructed in the original version of the conformal thin-sandwich
formalism.
