We investigate the apparent discrepancy between gas and dust outer radii derived from millimeter observations of protoplanetary disks. Using 230 and 345 GHz continuum and CO J = 3–2 data from the Submillimeter Array for four nearby disk systems (HD 163296, TW Hydrae, GM Aurigae, and MWC 480), we examine models of circumstellar disk structure and the effects of their treatment of the outer disk edge. We show that for these disks, models described by power laws in surface density and temperature that are truncated at an outer radius are incapable of reproducing both the gas and dust emission simultaneously: the outer radius derived from the dust continuum emission is always significantly smaller than the extent of the molecular gas disk traced by CO emission. However, a simple model motivated by similarity solutions of the time evolution of accretion disks that includes a tapered exponential edge in the surface density distribution (and the same number of free parameters) does much better at reproducing both the gas and dust emission. While this analysis does not rule out the disparate radii implied by the truncated power law models, a realistic alternative disk model, grounded in the physics of accretion, provides a consistent picture for the extent of both the gas and dust.