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In this work we present simple, physics-based models for two effects that have been noted in the fully depleted CCDs that are presently used in the Dark Energy Survey Camera. The first effect is the observation that the point-spread function increases slightly with the signal level. This is explained by considering the effect on charge-carrier diffusion due to the reduction in the magnitude of the channel potential as collected signal charge acts to partially neutralize the fixed charge in the depleted channel. The resulting reduced voltage drop across the carrier drift region decreases the vertical electric field and increases the carrier transit time. The second effect is the observation of low-level, concentric ring patterns seen in uniformly illuminated images. This effect is shown to be most likely due to lateral deflection of charge during the transit of the photogenerated carriers to the potential wells as a result of lateral electric fields. The lateral fields are a result of space charge in the fully depleted substrates arising from resistivity variations inherent to the growth of the high-resistivity silicon used to fabricate the CCDs.