A directive source integral equation (DSIE) approach is proposed for the analysis of scattering from essentially convex impenetrable objects. The DSIE augments the conventional equivalent sources located on the surface with fictitious electric and magnetic currents placed inside the volume originally occupied by the scatterer. These electric and magnetic currents are designed to absorb and suppress the radiation of the on-surface equivalent sources towards the interior of the scatterer. Introduction of such artificial absorbing shields is advocated to confine the field interactions to the scatterer surface and reduce the coupling between the distant parts of the object, thus facilitating development of fast solvers. The DSIE also resolves the non-uniqueness problem of the electric field integral equation by eliminating the internal resonances.