This paper discusses two combinatorial problems in stability theory. First we prove a partition result for subsets of stable models: for any A and B, we can partition A into |B|$^{< \kappa(T)}$ pieces, $\langle$ A$_i \mid i$ < |B|$^{< \kappa(T)}\rangle$, such that for each $A_i$ there is a B$_i \subseteq$ B where |B$_i$| < $\kappa$(T) and A$_i$ $\&2ADD;$ $\underset{B_i}$ B. Second, if A and B are as above and |A| > |B|, then we try to find A' $\subset$ A and B' $\subset$ B such that |A'| is as large as possible, |B'| is as small as possible, and A' $\&2ADD;$ $\underset{B'}$ B. We prove some positive results in this direction, and we discuss the optimality of these results under ZFC + GCH.