This study presents a new approach to the control problem of single-phase switch-mode rectifiers. The proposed approach is based on a particular model predictive control scheme, incorporated with soft constraints for the errors of the key control targets. This control system is free of PI controllers, which are responsible for poor dynamic performance. Control objectives of sinusoidal input current, approximately unity input power factor, and output voltage regulation are successfully met under both steady state and load or setpoint changes. Considering the significant advantages of multilevel operation, the reflected AC side voltage exhibits an appropriate three-level modulation. The developed control strategy involves improved performance compared with a model-based sliding mode one. The theoretical analysis is validated by measurements on a laboratory prototype, illustrating the feasibility and suitability of the proposed controller for this type of rectifiers.