The stability of the air-water interface with piecewise linear velocity profiles in the air and the water is analysed to study the effect of shear in the water on the generation of waves by wind. This simple formulation reduces the eigenvalue problem to the solution of a quartic equation, which facilitates the exploration of the dependence on the various physical parameters. The results indicate that the presence of water shear tends to enhance the Kelvin-Helmholtz-type instability and to lessen the Miles-type mechanism. In addition, the presence of water shear leads to a selection rule by which the growth of certain short wave components is suppressed. This may be relevant to high-frequency radar imaging of the ocean.