We investigate the theoretical limitations of applying statistical bias corrections to general circulation model data prior to downscaling with a regional climate model (RCM). Two methods from recent literature are compared: linear (LC) and quantile-quantile (QQ) corrections. An LC method is limited to correcting biases only in the distribution mean but retains all first-order spatial and intervariable dependencies. Conversely, the QQ method corrects any bias in the distribution function but cannot retain intervariable dependencies and adds variability to smooth spatial fields. An RCM's boundary relaxation scheme dampens the effect of imbalanced variables but may not remove the spurious variability from the QQ method. Case study results of precipitation over a South African river catchment show that both correction methods improve RCM-simulated monthly climatology, but the QQ correction creates a 20% bias in interannual monthly variability. We recommend the LC method as an effective bias correction for RCM inputs.