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A simple method to compute QED bound state properties is presented, in whichbinding energy effects are treated non-perturbatively. It is shown that to takethe effects of all ladder Coulomb photon exchanges into account, one can simplyperform the derivative of standard QED amplitudes with respect to the externalmomentum. For example, the derivative of the light-by-light scatteringamplitude gives an amplitude for orthopositronium decay to three photons whereany number of Coulomb photon exchanges between the e-e+ is included.  Various applications are presented. From them, it is shown that bindingenergy must be treated non-perturbatively in order to preserve the analyticityof positronium decay amplitudes.  Interesting perspectives for quarkonium physics are briefly sketched.Comment: LaTeX, 23 pages, 16 figures. Minor corrections. Some comments adde

A NEW BASIS FOR QED BOUND STATE COMPUTATIONS