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Precipitation patterns along cold fronts can exhibit a variety of morphologies including narrow cold-frontal rainbands and core-and-gap structures. A three-dimensional primitive equation model is used to investigate alongfront variability of precipitation in an idealized baroclinic wave. Along the poleward part of the cold front, a narrow line of precipitation develops. Along the equatorward part of the cold front, precipitation cores and gaps form. The difference between the two evolutions is due to differences in the orientation of vertical shear near the front in the lower troposphere: at the poleward end the along-frontal shear is dominant and the front is in near-thermal wind balance, while at the equatorward end the cross-frontal shear is almost as large. At the poleward end, the thermal structure remains erect with the front well defined up to the midtroposphere, hence updrafts remain erect and precipitation falls in a continuous line along the front. At the equatorward end, the cores form as undulations appear in both the prefrontal and postfrontal lighter precipitation, associated with vorticity maxima moving along the front on either side. Cross-frontal winds aloft tilt updrafts, so that some precipitation falls ahead of the surface cold front, forming the cores. Sensitivity simulations are also presented in which SST and roughness length are varied between simulations. Larger SST reduces cross-frontal winds aloft and leads to a more continuous rainband. Larger roughness length destroys the surface wind shift and thermal gradient, allowing mesovortices to dominate the precipitation distribution, leading to distinctive and irregularly shaped, quasi-regularly spaced precipitation maxima.