Many companies offer discounts on one-way rentals while other major companies do not offer one-way rentals at all. You need to do some research on which companies offer one-way truck rentals and which do not.
The best way to do research on who offers one-way truck rentals is to do an Internet search engine search for "moving truck rentals" and then compare prices. You can also call local moving truck rental companies in your area to get information about one-way truck rentals for moving.
If you want to do your own packing but don't feel like driving your belongings to your new location, you may want to consider a Upack type of moving company who will drive your belongings to their new location in a truck or moving pod. You are responsible for loading and unloading your belongings, but this type of moving truck rental is becoming increasingly popular for one-way moves. A little more expensive in price but well worth it if you don't want the hassle of driving a truck from one city to another.