A previous attempt to integrate geological, geodetic, and observed seismicity data into a probabilistic-hazard source model predicted a rate of magnitude 6 to 7 earthquakes significantly greater than that observed historically. One explanation was that the discrepancy, or apparent earthquake deficit, is an artifact of the upper magnitude limit built into the model. This was controversial, however, because removing the discrepancy required earthquakes larger than are seen in the geological record and larger than implied from empirical relationships between fault dimension and magnitude. Although several articles have addressed this issue, an alternative, integrated source model without an apparent deficit has not yet appeared. We present a simple geologically based approach for constructing such a model that agrees well with the historical record and does not invoke any unsubstantiated phenomena. The following factors are found to be influential: the b-value and minimum magnitude applied to Gutenberg-Richter seismicity; the percentage of moment released in characteristic earthquakes; a round-off error in the moment-magnitude definition; bias due to historical catalog incompleteness; careful adherence to the conservation of seismic moment rate; uncertainty in magnitude estimates obtained from empirical regressions; allowing multi-segment ruptures (cascades); and the time dependence of recurrence rates. The previous apparent deficit is shown to have resulted from a combination of these factors. None alone caused the problem nor solves it. The model presented here is relatively robust with respect to these factors.