DC-AC rectifiers with reduced numbers of switches, in order to reduce cost, weight, volume and switching losses (especially for low-power applications), have been presented and discussed in the literature. These converters are less exposed to semiconductor switch damage and exhibit lower common-mode currents. However, they have several disadvantages when compared with conventional six-switch three-phase (SSTP) rectifiers, such as dc-link capacitor voltage fluctuation, reduced input ac supply utilisation factor, and unbalanced three-phase input currents. This paper proposes new designs for four-switch three-phase (FSTP) and two-switch single-phase rectifiers (TSSP). This paper explains the normal operation, and proposes beneficial comparisons and performance evaluation, of the proposed rectifiers. In addition, proper control design for the proposed converters is presented with sliding mode control (SMC).