  We study minimal $\mathbb{Z}^d$-Cantor systems and the relationship between
their speedups, their collections of invariant Borel measures, their associated
unital dimension groups, and their orbit equivalence classes. In the particular
case of minimal $\mathbb{Z}^d$-odometers, we show that their bounded speedups
must again be odometers but, contrary to the 1-dimensional case, they need not
be conjugate, or even isomorphic, to the original.
