We study the problem of managing an inventory system with two supply sources which differ in their lead times and unit prices. We consider a simple class of policies called Tailored Base-Surge (TBS) policies for managing this system. These policies order a constant amount in every period from the slow supplier and order up to a target level in every period from the faster and more expensive supplier. We prove an asymptotic convergence result on the cost of an optimal TBS policy as the unit inventory holding cost goes to zero while keeping the service level constant and simultaneously increasing the unit cost of procurement from the faster supplier. The asymptotic value of cost also serves as an upper bound on the optimal cost of all dual sourcing systems with the same service level and product of unit procurement and holding cost. This bound is better than the previously best known upper bound on the cost of an optimal dual sourcing policy in the same regime.