The present paper addresses the short-term distribution of zero-crossing wave heights in intermediate and shallow water depths. New physical insights are provided regarding the effects of nonlinearity, directionality, reduced effective water depth and finite spectral bandwidth. These are demonstrated through the analysis of a large database of experimental simulations of short-crested sea-states on flat bed bathymetries. A new wave height model is proposed building upon these physical insights and is calibrated using the experimental data. Independent comparisons between field measurements and the proposed model indicate that it is appropriate to a wide range of incident wave conditions and that it provides considerable improvement over existing models.