This paper analyzes features and problems related to the application of the simplex sliding mode control to systems with mono-directional actuators and integrators in the input channel. The plain use of the method formulated in previous contributions results in unacceptable behaviors, such as control laws (the output of the mono-directional actuators), which increase without bounds. A nontrivial modification of the original algorithm is proposed; the new simplex strategy allows the fulfillment of the control objectives by means of bounded inputs from the actuators. (C) 2011 Elsevier Ltd. All rights reserved.