Four new exchange potentials (the semiclassical exchange approximation, the asymptotically adjusted free-electron-gas exchange approximation, the second-order free-electron-gas exchange approximation, and the high-energy exchange approximation) are derived. Calculations are performed for elastic electron scattering from helium and argon. The results are compared to one another and to calculations using Hara's free-electron-gas approximation and the exact nonlocal exchange potential. Three of the approximations to exchange are in good agreement with the exact exchange-except at very low energy-but are much easier to use. Thus they should be very useful in electron-atom and electron-molecule scattering calculations.