  We present a substantial generalization of the equinumeracy of grand Dyck
paths and Dyck-path prefixes, constrained within a band. The number of
constrained paths starting at level $i$ and ending in a window of size $2j+2$
is equal to the number starting at level $j$ and ending in a window of size
$2i+2$ centered around the same point. A new encoding of lattice paths provides
a bijective proof.
