Waveriders demonstrate good aerodynamic performance and thus are of special interest for hypersonic applications, especially for engine-airframe integration. The osculating cones waverider method is a generic shock-based derived waverider design method that allows prescribing a wide variety of flowfields at the inlet of the engine of the hypersonic vehicle. Previous osculating cones waveriders methods assumed that along the streamlines within the waverider shock layer, the pressure gradients in the azimuthal direction were negligible, and thus neglected it into the design process. The focus of this work is to investigate the magnitude of those pressure gradients, and integrate those into a new osculating cones waverider design method by modifying the derivation of the lower surface (streamsurface). The geometries resulting from the design code are to be compared with the previous solutions. The flowfield and aerodynamic performance predicted by the design code are compared with the results from Computational Fluid Dynamics simulations.