Motivated by an observed relationship between marine low cloud cover and surface wind speed, this study investigates how vertical wind shear affects trade-wind cumulus convection, including shallow cumulus and congestus with tops below the freezing level. We ran large-eddy simulations for an idealised case of trade-wind convection using different vertical shears in the zonal wind. Backward shear, whereby surface easterlies become upper westerlies, is effective at limiting vertical cloud development, which leads to a moister, shallower and cloudier trade-wind layer. Without shear or with forward shear, shallow convection tends to deepen more, but clouds tops are still limited under forward shear. A number of mechanisms explain the observed behaviour: First, shear leads to different surface wind speeds and, in turn, surface heat and moisture fluxes due to momentum transport, whereby the weakest surface wind speeds develop under backward shear. Second, a forward shear profile in the subcloud layer enhances moisture aggregation and leads to larger cloud clusters, but only on large domains that generally support cloud organization. Third, any absolute amount of shear across the cloud layer limits updraft speeds by enhancing the downward-oriented pressure perturbation force. Backward shear — the most typical shear found in the winter trades — can thus be argued a key ingredient at setting the typical structure of the trade-wind layer.