Let J (M2 ) denote the -ideal associated with two-dimensional Miller forcing. We show that it is relatively consistent with ZFC that the additivity of J (M2 ) is bigger than the covering number of the ideal of the meager subsets of . We also show that Martin's Axiom implies that the additivity of J (M2 ) is 2 . Finally we prove that there are no analytic infinite maximal antichains in any finite product of P()/fin.