The general problem of double injection into a perfect insulator, free of traps and of thermal free carriers, does not yield to a complete, analytical description. A complete solution is presented for the limiting cases of very large and very small σR, where σR is the electron‐hole recombination cross section. The first situation corresponds to a pair of back‐to‐back, one‐carrier, space‐charge‐limited currents, the second to an injected plasma. The I‐V characteristics obtained in these two limits agree precisely with the earlier general analytical result of Parmenter and Ruppel. For intermediate values of σR the Regional Approximation method is used to obtain an approximate solution. The field and density distributions, obtained for large, intermediate, and small values of σR, are the first available for this problem. The constant‐lifetime and bimolecular‐recombination injected plasmas are compared and found to have remarkably similar distributions.