The overconvergent modular symbols of Stevens provide a natural framework for computing p-adic L-functions of newforms, but the modular symbols (and p-adic L-functions) attached to ordinary Eisenstein series are essentially trivial. Working with a larger space of pseudo-distributions, we construct non-trivial Eisenstein symbols and compute their p-adic L-functions. As a corollary, we compute the p-adic L-function of the "evil twin" Eisenstein series of critical slope. If time permits, I'll discuss work in progress on computing the symmetric square p-adic L-function at Eisenstein points on the eigencurve, as well as applications.