Constrained receding horizon controllers are often designed to govern the system state to some desired set-point subject to input constraints. This paper presents a class of receding horizon controllers which satisfy such constraints via the inclusion of a 'recentred barrier function'. The significance of such a controller is that hard constraints are replaced with penalty type soft constraints. The resulting control law is cautious near constraint boundaries with the degree of caution being determined by a positive weighting parameter. This approach is applicable to general convex objective functions with convex inequality constraints. We illustrate this idea by way of an example application to linear discrete-time plant models with linear and convex quadratic static input constraints