We consider the question of finding deep cuts from a model constructed with two rows of a simplex tableau. To do that, we show how to reduce the complexity of setting up the polar of such model from a quadratic number of integer hull computations to a linear number of integer hull computations. Furthermore we present an algorithm that avoids computing integer hulls. A polynomial running time is not guaranteed but computational results show that the algorithm runs quickly in practice.
March 2010, revised September 2012. To appear in Mathematical Programming A.