Previous studies of slot film cooling have mainly concentrated on a flow geometry so arranged that the slot is flush in the containing wall. It is known that when the total pressure head of the injected flow is less than the free stream head, separation from the front of the slot is tangential to the wall (the so-called ‘lid’ effect). This phenomenon limits the mass flow from the slot which in turn limits the effectiveness of the cooling. An appealing strategy to enhance the mass flow is to force a non-zero angle of separation from the upstream end of the slot by geometrical means. The present study considers the influence of the geometry on mass flow and suggests possible improvements for the mean flow characteristics. Asymptotic analysis based on inviscid flow theory is used to derive a nonlinear singular integrodifferential equation (NLSIDE) for the height of the separating streamline. This equation is then solved numerically and the mass flow characteristics determined for various geometries.