  We compute that the growth of the origin occupation-time variance up to time
t in dimension d=2 with respect to asymmetric simple exclusion in equilibrium
with density 1/2 is in a certain sense at least t(log(log t)) for general
rates, and at least t(log t)^{1/2} for rates which are asymmetric only in the
direction of one of the axes. These estimates are consistent with conjectures
with respect to the transition function and variance of 'second-class'
particles.
