Using a parameterised function for the mass loss at the base of the post-shock region, we have constructed a formulation for magnetically confined accretion flows which avoids singularities, such as the infinity in density, at the base associated with all previous formulations. With the further inclusion of a term allowing for the heat input into the base from the accreting white dwarf we are able also to obtain the hydrodynamic variables to match the conditions in the stellar atmosphere. (We do not, however, carry out a mutually consistent analysis for the match). Changes to the emitted X-ray spectra are negligible unless the thickness of mass leakage region at the base approaches or exceeds one percent of the height of the post-shock region. In this case the predicted spectra from higher-mass white dwarfs will be harder, and fits to X-ray data will predict lower white-dwarf masses than previous formulations.
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