We examine the possibility of extracting non-Gaussian sources from two-particle correlations in heavy-ion reactions. Non-Gaussian sources have been predicted in a variety of model calculations and may have been seen in various like-meson pair correlations. As a tool for this investigation, we have developed an improved imaging method that relies on a Basis spline expansion of the source functions with an improved implementation of constraints. We examine under what conditions this improved method can distinguish between Gaussian and non-Gaussian sources. Finally, we investigate pion, kaon, and proton sources from the p-Pb reaction at 450 GeV/nucleon and from the S-Pb reaction at 200 GeV/nucleon studied by the NA44 experiment. Both the pion and kaon sources from the S-Pb correlations seem to exhibit a Gaussian core with an extended, non-Gaussian halo. We also find evidence for a scaling of the source widths with particle mass in the sources from the p-Pb reaction.Comment: 16 pages, 15 figures, 5 tables, uses RevTex3.