The ‘Not to Exceed’ Estimate. When you ask the mover to provide an opinion of the cost, one option is a ‘Binding Not-to-Exceed’ estimate. With this type of estimate, if your actual weight is more than the written estimate, you’ll pay for only the amount of the estimate. And if your actual weight is less than the estimate, then your cost can actually go down. And get full replacement ‘valuation’ coverage to protect your goods in the event of any damage. Next: Things not to pack.