Plenty retailers handling fresh produce face the following operational problem in their distribution centers: Pallets of food assembled during the day according to the demands of supermarkets are to be intermediately stored overnight. To save cooling costs, deep-lane storage in some compact storage system is applied, from which the pallets are to be retrieved the next morning when the trucks servicing the supermarkets are to be loaded under great time pressure. To enable an efficient retrieval process, we seek storage assignments defining the put-away of pallets in the deep-lane storage system, such that blockings, i.e., a pallet with later retrieval time is placed in front of another pallet with higher priority in the same lane, are avoided. Most deep-lane storage systems allow only a front access, whereas novel systems can be loaded and unloaded from two sides. We formalize both resulting storage assignment problems, investigate computational complexity, introduce solution procedures, and quantify the increase in flexibility promised by a two-sided access. Our computational results reveal that especially if truck arrivals are hard to anticipate due to a considerable amount of uncertainty, two-sided systems greatly reduce blockings.