A one-dimensional model has been used to study the effects of exospheric temperature, methane and water influx, ionospheric outflow, and electron precipitation on the composition and structure of the ionosphere of Uranus. Peak ion concentrations range from 103 to 106 cm-3 with a wide variation in peak altitude, which depends strongly on the exospheric temperature. In all the cases we considered, H+ is the major ion in the topside ionosphere. At altitudes near or below the peak, H3+ and CH5+ can dominate, depending on the magnitude of CH4 and H2O influx. Atomic hydrogen column depths above the methane absorbing layer exceed 1017 cm-2 and can produce large (400 R) emissions of resonantly scattered Lyman-alpha. In the sunlit polar cap, electron precipitation with energy fluxes of 0.6 to 1.0 erg cm-2 s-1 results in direct production of Lyman-alpha emissions that exceed 1 kR.