  We establish upper bounds for the spectral gap of the stochastic Ising model
at low temperatures in an n-by-n box with boundary conditions which are not
purely plus or minus; specifically, we assume the magnitude of the sum of the
boundary spins over each interval of length n in the boundary is bounded by
\delta n, where \delta < 1. We show that for any such boundary condition, when
the temperature is sufficiently low (depending on \delta), the spectral gap
decreases exponentially in n.
