  We present a new method of gap control in two-dimensional periodic systems
with the perturbation consisting of a second-order differential operator and a
family of narrow potential `walls' separating the period cells in on direction.
We show that under appropriate assumptions one can open gaps around points
determined by dispersion curves of the associated `waveguide' system, in
general any finite number of them, and to control their widths in terms of the
perturbation parameter. Moreover, the distinctive feature of those gaps is that
their edge values are attained by the corresponding band functions at internal
points of the Brillouin zone.
