Recently, laboratory measurements of wind-generated deepwater waves have been made by Ramamonjiarisoa and Coantic and by Lake and Yuen. They found that the phase velocity was independent of frequency at least for a certain range of frequencies. One explanation for this unexpected result has been given by Longuet-Higgins, who made a specific assumption about the directional wave number spectrum. Another tentative explanation ascribes the observed constancy to nonlinear effects. In this note, model spectra based on these explanations are studied, and it is shown how a relatively simple measurement of the cross-spectral density at 90¿ to the wind direction could discriminate between these different models.