The iceberg cube mining computes all cells v, corresponding to GROUP BY partitions, that satisfy a given constraint on aggregated behaviors of the tuples in a GROUP BY partition. The number of cells often is so large that the result cannot be realistically searched without pushing the constraint into the search. Previous works have pushed antimonotone and monotone constraints. However, many useful constraints are neither antimonotone nor monotone. We consider a general class of aggregate constraints of the form f(v)θσ, where f is an arithmetic function of SQL-like aggregates and θ is one of <, ≤, ≥ >. We propose a novel pushing technique, called divide-and-approximate, to push such constraints. The idea is to recursively divide the search space and approximate the given constraint using antimonotone or monotone constraints in subspaces. This technique applies to a class called separable constraints, which properly contains all constraints built by an arithmetic function f of all SQL aggregates.