The operation of an unconventional, power-symmetric nonlinear optical loop mirror (NOLM) is investigated. Its principle is based on the creation of a polarization asymmetry between the counterpropagating beams, through the use of a quarter-wave plate and highly twisted fiber in the loop. Using a very intuitive approach, we propose a simple although comprehensive description of the NOLM operation. By adjusting the angle of the quarter-wave plate, the interferometer can be tuned continuously from non-power-dependent operation to nonlinear switching, in a very convenient way. Experimental results confirm theoretical predictions. The properties of the proposed NOLM design make it very attractive for various applications, like pedestal suppression and amplitude regularization of optical pulse trains.