Detections of deuterium in high-redshift Lyman limit absorption systems along the line of sight to QSOs promise to reveal the primordial deuterium abundance. At present, the deuterium abundances (D/H) derived from the very few systems observed are significantly discordant. Assuming the validity of all the data, if this discordance does not reflect intrinsic primordial inhomogeneity, then it must arise from processes operating after the primordial nucleosynthesis epoch. We consider processes that might lead to significant deuterium production or destruction and yet allow the cloud to mimic a chemically unevolved system. These processes include, for example, anomalous/stochastic chemical evolution and D/4He photodestruction. In general, we find it unlikely that these processes could have significantly altered D/H in Lyman limit clouds. We argue that chemical evolution scenarios, unless very finely tuned, cannot account for significant local deuterium depletion since they tend to overproduce 12C, even when allowance is made for possible outflow. Similarly, D/4He photodestruction schemes engineered to locally produce or destroy deuterium founder on the necessity of requiring an improbably large γ-ray source density. Future observations of D/H in Lyman limit systems may provide important insight into the initial conditions for the primordial nucleosynthesis process, early chemical evolution, and the galaxy formation process. © 1997. The American Astronomical Society. All rights reserved.