  We explore the effect of transverse confinement on the stability of a
Bose-Einstein condensate (BEC) loaded in a shaken one-dimensional or
two-dimensional square lattice. We calculate the decay rate from two-particle
collisions. We predict that if the transverse confinement exceeds a critical
value, then, for appropriate shaking frequencies, the condensate is stable
against scattering into transverse directions.
