I present two cases of sequential trade models of market microstructure with heterogeneous information partitions. First, the trader with information can infer the true value only under certain realizations. The main result is that the equilibrium outcomes look quite different from the literature, suggesting that the information assumptions may be a delicate issue to consider in these models. In the second example I adapt a non-partitional information approach from Geanakoplos (1989). When the informed investor does not observe this signal, she does not infer whether the value of the asset is low or high. Here positive spreads may not lead to trade.