The Kelvin–Helmholtz problem deals with the stability of fluids where both shear and stable stratification are restricted to a layer. In observed shear instability in the atmosphere, stable stratification rarely disappears outside the shear zone. In order to get some idea of the implications of this fact, I have investigated the stability properties of a particularly simple configuration: a Helmholtz velocity profile in a continuously stratified, infinite Boussinesq fluid. For a basic discontinuity 2U and Brunt-Väisälä frequency N, I find that perturbations with horizontal wavenumbers k, such that k2>N2/(2U2), are unstable and decay away from the shear zone. In addition, the shear zone is capable of supplying energy to neutral internal gravity waves, for which k2<N2/U2, which propagate away from the shear zone. A particular wavenumber, k2 = N2/(2U2), is shown to be most efficient at carrying energy away from the shear zone. However, additional calculations suggest that for the configuration considered, instabilities ought to be more effective than waves in smoothing the original shear. Comparison with observations suggests, on the other hand, that the waves dominate observed disturbances. The reasons for this are discussed. It is suggested that the waves are enhanced by reflections from the earth's surface which were ignored in the calculations.