Stationary models for accretion disc-boundary layer systems based on the slim disc approximation with radial radiative and advective energy transport included are constructed. Arguing that application of even the modified causal alpha -prescription in the boundary layer is questionable, we resort to the classical form of Prandtl's mixing length theory for a parametrization of the viscosity. It is shown that the coupling between pressure and viscosity inherent in the alpha -prescription is responsible for characteristic features of the boundary layer solutions in the standard approach. This coupling is relaxed when using the viscosity proposed in this paper. Then the boundary layer structure becomes significantly different from standard solutions, and major drawbacks of the alpha -model, such as the coexistence of high viscosity and rigid rotation, do not occur. The properties of the new boundary layer-disc solutions are demonstrated by application to non-magnetic cataclysmic variables.