An extension of earlier computations on deep‐water gravity wave instabilities up to a wave steepness of 0.434 is performed to compare the relative strength of class I versus class II instabilities. The three‐dimensional class II,m=1 instabilities are still predominant. However, as the steepness increases, the difference between the growth rates of two‐dimensional and three‐dimensional perturbations decreases rapidly and becomes negligible around a 0.43 wave steepness.