Abstract Radial measures of efficiency estimated using linear programming (LP) methods can be biased since slack in the constraints defining the technology suggests that at least one input can be reduced, or one output can be expanded, even though a firm is deemed to be “technically efficient.” In this paper, we propose a directional slacks-based measure of technical inefficiency to account for the potential of slack in technological constraints. When no such slacks exist, directional slacks-based inefficiency collapses to the directional technology distance function. Our proposed measure helps to generalize some of the existing slacks-based measures of inefficiency. We examine the financial services provided by Japanese cooperative Shinkin banks, and estimate their inefficiency during the period 2002–2005. This inefficiency declined slightly during the period. We thus propose that slack is an important source of inefficiency which is often not captured by the directional technology distance function.