It has recently been shown that spectrum analysis of instantaneous power can provide sensitive online detection of rotor faults in induction motors compared with current, torque, speed, or vibration spectrum analysis. However, it was reported that monitoring of the twice slip frequency, 2sfs, components induced by the fundamental component can produce false rotor fault alarms due to asymmetry in the rotor or low frequency load oscillations. In this paper, the rotor fault components induced in the power spectrum by the stator fifth and seventh space harmonics are derived to evaluate their immunity to false alarms. It is shown that the (6 - 8s) f(s) component can provide reliable detection of rotor faults under cases where existing methods produce false alarms. An experimental study performed on custom built rotor samples shows that the new components are capable of detecting rotor faults immune to false alarms produced by rotor axial air ducts, rotor anisotropy, and low frequency load oscillations for cases where existing methods fail. The components derived in this paper can also be applied to vibration, speed, torque, or acoustic monitoring for reliable detection of rotor faults.