In this paper, we establish two combinatorial bounds related to the separation problem for sets of n pairwise disjoint translates of convex objects: 1) there exists a line which separates one translate from at least n — con translates, for some constant c that depends on the shape of the translates and 2) there is a function f such that there exists a line with orientation or f() which separates one translate from at least 3n/4-4 translates, for any orientation (f is defined only by the shape of the translate). We also present an O(n log (n+k)+k) time algorithm for finding a translate which can be separated from the maximum number of translates amongst sets of n pairwise disjoint translates of convex k-gons.