The exterior Dirichlet problem can be formulated in terms of either a first‐kind or a second‐kind integral equation for the normal velocity at the surface of the scatterer. However, neither of the standard equations has a unique solution at all frequencies. It is shown here that a third formulation, obtained simply by forming a linear combination of the two original equations, does give the correct solution uniquely at all frequencies. Similarly, the exterior Neumann problem can be described by a first‐ or second‐kind equation for the pressure at the surface, neither of which has a unique solution at all frequencies; but a linear combination of the two equations again yields the correct solution uniquely. Numerical results for the analogous problem in electromagnetics indicate that the new formulations should be well suited for practical computation.