Constrained receding-horizon predictive control (CRHPC) is intended for demanding control applications where conventional predictive control designs can fail. The idea behind CRHPC is to optimise a quadratic function over a ‘costing horizon’ subject to the condition that the output matches the reference value over a further constraint range. Theorems show that the method stabilises general linear plants (e.g. unstable, nonminimum-phase, dead-time). Simulation studies demonstrate good behaviour with even nearly unobservable systems (where generalised predictive control is ineffective) and that control-costing is a particularly effective tuning parameter.