In this paper two multiphase open-end asymmetric current source rectifiers are proposed. These new rectifiers are derived from an improved multiphase crossed switches current source converter, named X-type CSC. The X-type CSC presents independent phase operation, higher efficiency (when compared to similar ones), and high AC output voltage waveform quality. Being used exclusively as a rectifier, the X-type CSC can be even further improved. One can remove the active switch from the the series connection of active switch and a diode configuration, resulting in an asymmetric converter with only half of the active switches from the full controlled topology. With this modification, the efficiency increases and the cost is reduced. The multiphase asymmetric X-type current source rectifiers are presented with their respective pulse-width and space vector modulation generalization. Simulation and experimental results are presented in order to validate the theoretical approach. At last, a comparison of the studied topologies is made and the best converter is selected.