The Brownian Passage Time (BPT) model for earthquake recurrence is modified to include transient deformation due to either viscoelasticity or deep post seismic slip. Both of these processes act to increase the rate of loading on the seismogenic fault for some time after a large event. To approximate these effects, a decaying exponential term is added to the BPT model's uniform loading term. The resulting interevent time distributions remain approximately lognormal, but the balance between the level of noise (e.g., unknown fault interactions) and the coefficient of variability of the interevent time distribution changes depending on the shape of the loading function. For a given level of noise in the loading process, transient deformation has the effect of increasing the coefficient of variability of earthquake interevent times. Conversely, the level of noise needed to achieve a given level of variability is reduced when transient deformation is included. Using less noise would then increase the effect of known fault interactions modeled as stress or strain steps because they would be larger with respect to the noise. If we only seek to estimate the shape of the interevent time distribution from observed earthquake occurrences, then the use of a transient deformation model will not dramatically change the results of a probability study because a similar shaped distribution can be achieved with either uniform or transient loading functions. However, if the goal is to estimate earthquake probabilities based on our increasing understanding of the seismogenic process, including earthquake interactions, then including transient deformation is important to obtain accurate results. For example, a loading curve based on the 1906 earthquake, paleoseismic observations of prior events, and observations of recent deformation in the San Francisco Bay region produces a 40% greater variability in earthquake recurrence than a uniform loading model with the same noise level.