The authors have investigated the effects of spatial and temporal variations in the heating of cool loop models in an attempt to explain the net redshifts that are observed on the Sun. In none of the situations considered are the induced flows able to satisfactorily reproduce the observations. In the case of asymmetric heating, the end-to-end flows can be as fast as 20 km s-1, but the downflowing leg is neither appreciably faster nor appreciably brighter than the upflowing leg; no net redshift is produced. In the case of symmetric heating, the downflows can also be large, but they are restricted to temperatures that are well below 105K. Neither situation would give rise to the ⪆7 km s-1 disk-averaged redshifts seen in emission lines of species like C IV.