Three new applications of the hodograph method to the problem of gas and water cresting towards horizontal wells are presented: (1) A numerical technique, based on the hodograph method, is used to find the shape of the oil/water interface and values of critical heights for the problem of water cresting towards a horizontal well beneath an impermeable plane. (2) By correct implementation of the boundary conditions in the lateral edge drive model, a hodograph solution is found for which the water crest tends to a horizontal asymptote far from the well, rather than tending towards a parabolic curve as in previous approaches. The solution yields integral representations for the lengths of boundary segments and enables an explicit expression for the critical rate to be derived in terms of the distance to the constant potential boundary. (3) The problem of simultaneous gas and water cresting towards a horizontal well in a thin oil column reservoir is solved using the hodograph method, providing shapes of the free interfaces and an expression for the optimal placement of the well with respect to the interfaces.