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.