If a motion aftereffect (MAE) for given adaptation conditions has a duration T s, and the eyes are closed after adaptation during a waiting period tw=T s before testing, an unexpected MAE of a 'residual' duration TrT s is experienced. This effect is called 'storage' and it is often quantified by a storage factor sigma=TrT/T, which can reach values up to about 0.7-0.8. The phenomenon and its name have invited explanations in terms of inhibition of recovery during darkness. We present a model based on the opposite idea, that an effective test stimulus quickens recovery relative to darkness or other ineffective test stimuli. The model is worked out in mathematical detail and proves to explain 'storage' data from the literature, on the static MAE (sMAE: an MAE experienced for static test stimuli). We also present results of a psychophysical experiment with moving random pixel arrays, quantifying storage phenomena both for the sMAE and the dynamic MAE (dMAE: an MAE experienced for a random dynamic noise test stimulus). Storage factors for the dMAE are lower than for the sMAE. Our model also gives an excellent description of these new data on storage of the dMAE. The term 'storage' might therefore be a misnomer. If an effective test stimulus influences all direction tuned motion sensors indiscriminately and thus speeds up equalization of gains, one gets the storage phenomenon for free.