A slit viscometer to measure the viscosity of polymer melts under processing conditions is described. Along the slit a pressure drop is generated by applying a pressure at both the entrance and the exit. In this way the pressure in the center can be controlled independently of the shear rate. The pressure gradient in the slit is measured by means of three pressure transducers which are mounted in the region of fully developed flow. Results of pressure-dependent viscosity measurements on polystyrene, polyacrylonitrile-butadiene-styrene, and polypropylene are presented in a shear rate range of five decades. The flow curves obtained at different pressures and temperatures can be shifted onto a master curve. The shear thinning behavior of the three materials is adequately described with the generalized Cross-Carreau equation, while the zero shear viscosity is modeled with a generalized Arrhenius-W.L.F. relationship, incorporating a pressure dependency. Alternatively, it is possible to describe the zero shear viscosity in terms of the free volume fraction and the temperature.