We present an improved calculation of the vertical structure and ultraviolet spectrum of a dissipative accretion disk in an active galactic nucleus (AGN). We calculate model spectra in which the viscous stress is proportional to the total pressure, the gas pressure only, and the geometric mean of the radiation and gas pressures. As a result of a more complete treatment of absorptive opacity, we find greater overall spectral curvature than Laor & Netzer did, as well as larger amplitudes in both the Lyman and He II photoionization edges. The local blackbody approximation is not a good description of the near-UV spectrum. With relativistic corrections (appropriate to nonrotating black holes) included, we find that the near-UV spectrum hardens with increasing (m) over dot/m(8) (m is the accretion rate in Eddington units, m(8) the black hole mass in units of 10(8) M-circle dot). The near-UV spectrum is consistent with observations if (m) over dotm(8)(-1) similar to 10(-3), but disks this cold would have absorption features at the Lyman edge, which are never seen in real AGNs. The edge amplitude is reduced when (m) over dot /m(8) is larger, but then the near-UV slope is too hard to match observations. We conclude that models in which conventional disks orbit nonrotating black holes do not adequately explain UV continuum production in AGNs.