Two of the four wells monitored near Parkfield, California, during 1985 showed water level rises beginning three days before the M4 6.1 Kettleman Hills earthquake. In one of these wells, the 3.0 cm rise was nearly unique in five years of water level data. However, in the other well, which showed a 3.8 cm rise, many other changes of comparable size have been observed. Both wells that did not display pre-earthquake rises tap partially confined aquifers that cannot sustain pressure changes due to tectonic strain having periods longer than several days. We evaluate the effect of partial aquifer confinement on the ability of these four wells to display water level changes in response to aquifer strain. Although the vertical hydraulic diffusivities cannot be determined uniquely, we can find a value of diffusivity for each site that is consistent with the site's tidal and barometric responses as well as with the rate of partial recovery of the coseismic water level drops. Furthermore, the diffusivity for one well is high enough to explain why the preseismic rise could not have been detected there. For the fourth well, the diffusivity is high enough to have reduced the size of the preseismic signal as much as 50%, although it should still have been detectable. Imperfect confinement cannot explain the persistent water level changes in the two partially confined aquifers, but it does show that they were not due to volume strain. The pre-earthquake water level rises may have been precursors to the Kettleman Hills earthquake. If so, they probably were not caused by accelerating slip over the part of the fault plane that ruptured in that earthquake because they are of opposite sign to the observed coseismic water level drops.