The diffuse ionized gas (DIG), responsible for producing the faint but pervasive H(sub alpha), requires 15% of the power of all Galactic O stars for its ionization. No other source of ionization seems practical. The spectrum is strong in low stages of ionization (N II, SII), weak in (O III), and very weak in (O I) lambda 6300, at least in one well-observed direction, all significantly different from denser H II regions. We give low-density, low-excitation photoionization models that explain the observed spectrum. The lambda 6300 observation eliminates the simplest models for the DIG (Mathis 1986), in which neutral H extends beyond the edge of the very dilute stellar radiation field. Our present models include two components. One, representing the edges of interstellar H I clouds, extends to the point where H becomes neutral. In the second, the fraction of H(sup o) is not allowed to exceed 0.05 to 0.1. Both have very low values of the ionization parameter, or ratio of the number densities of ionizing photons to electrons. The ionization parameter required by our models is shown to be compatible with observed values of photon and electron densities in the diffuse interstellar medium. Interstellar dust is not important in either model. Predictions of the model are that the Galaxy is leaking about 4% of the ionizing radiation of at least the local O stars into the intergalactic medium, that (O II) lambda 3727 approximately equals 1.1 H(sub alpha), and that He(sup +)/H (sup +)) approximately equals 0.6 He/H. A major difficul ty of this picture is having ionizing radiation propagate from the ionizing stars in the plane of the Galaxy to the DIG. We suggest, as do Miller & Cox (1993), that the ionizing radiation from O stars produces holes or tunnels in the distribution of neutral H as seen from their positions, while we see a sky covered with H I sheets or filaments because we are not near a source of ionizing radiation. With our models, several interfaces between ionized and neutral gas are allowed before the observational limit on lambda 6300 is exceeded. Another difficulty is the gas-phase N(S(sup +))/N(H(sup o)) ratio toward the high-latitude star HD 93521 (Spitzer & Fitzpatrick 1993). We require (S/H) to be somewhat lower than solar, either because of depletion onto grains or a Galactic abundance gradient, so that the S(sup +) can be produced in each of separate H(sup o) and H(sup +) regions.