The net tunneling conductance of metal-insulator-metal tunnel junctions is studied using a distribution of barrier thicknesses consistent with interfacial roughness typical of state-of-the-art tunnel junctions. Moderate amounts of roughness cause the conductance to resemble that of much thinner and taller barriers. Fitting numerically generated conductance data that include roughness with models that assume a single-thickness barrier leads to erroneous results for both the barrier height and width. Rules of thumb are given that connect the roughness to the real space mean thickness and the thickness inferred from fitting the net conductance with traditional tunneling models.