An ansatz is proposed, complemented by appropriate selection rules, to estimate the convection velocity Uc of turbulent vortical structures in low Mach number, supersonic shear layers. The proposed scheme assumes that, for low supersonic convective Mach numbers, shocks will form in one of the two shear layer free streams. The strength of the shocks is estimated by assuming that the flow configuration, in a frame moving at the convection velocity Uc, is stationary with respect to perturbations in the mean flow quantities caused by the turbulent fluctuations. Given the shock strength, the convection velocity Uc and the associated convective Mach numbers are calculated by matching the estimated total pressure at stagnation points in the convected frame. Presently available data indicate a convection velocity Uc that is close to U1, or U2, the high and low speed stream velocities, respectively, with an empirical stream selection rule that Uc is closer to U1, when the low speed stream is subsonic, and closer to U2 when both streams are supersonic. With the proviso that the predicted shock-bearing stream is as suggested by the empirical stream selection rule, the experimentally observed values for Uc appear to be well accounted for by the proposed scheme. These results have important implications for supersonic mixing and hypersonic propulsion applications.