This paper addresses two potential problems that arise when measuring Farrell cost efficiency using linear programming methods. First, when an optimal solution to the cost function allows slack in the output constraints that define the technology it is possible to increase at least one output without increasing costs. Therefore, two firms might be deemed equally cost efficient even though one firm produces more of at least one output. Second, previous research has shown that when input prices vary across firms, it is possible for firms with higher costs to be deemed more cost efficient than firms who have lower costs. We present a new measure of cost efficiency that accounts for both of these potential problems. We illustrate our method using data on Japanese securities firms operating in the 2004 to 2006.