Methods of the present invention are designed to offer insurance to lessees of vehicles to cover up front, out-of-pocket lease expenses in the event of a total loss, e.g., theft, and preferably include steps performed by a vehicle leasing dealer as well as steps performed by one or more participating insurers. The steps are preferably performed with the aid of computing devices which are in communication. When the lease is prepared, the relevant information about the lease and the lessee is submitted by the lease dealer to the participating insurers. The insurers determine the cost of supplemental insurance based on this information and, if the cost is acceptable, offer insurance coverage to the lessee.