Once your shipment is picked up, you may incur storage costs if you change the delivery date. So try to make sure you're able to move into your new home on the scheduled date. Otherwise, you may wind up having to put your things into storage for one night, which will cost you money that you could have saved had you been more organized. There are other hidden costs to consider as well: Moving a difficult item like a piano may cost extra. You also may need to purchase extra insurance coverage for your high-priced art or hire special handlers for those items.