A description is given of a distorted-wave method for the solution of the Lippmann-Schwinger equation for electron-atom scattering. The integral equation is solved using a complete set of states defined by the direct static potential of the atom under investigation rather than using the usual plane-wave representation. Results for the static-exchange scattering of electrons from helium and argon show significantly improved convergence over plane-wave expansion techniques and are of sufficient accuracy to indicate that the method can be generalised to efficiently solve the multichannel Lippmann-Schwinger equation.