  We prove a law of large numbers for a class of $\Z^d$-valued random walks in
dynamic random environments, including non-elliptic examples. We assume for the
random environment a mixing property called \emph{conditional cone-mixing} and
that the random walk tends to stay inside wide enough space-time cones. The
proof is based on a generalization of a regeneration scheme developed by Comets
and Zeitouni for static random environments and adapted by Avena, den Hollander
and Redig to dynamic random environments. A number of one-dimensional examples
are given. In some cases, the sign of the speed can be determined.
