The advantages and limitations of multiple spin-echo sequences for non-Fourier encoding are investigated. Complications caused by improper encoding of alternate magnetization pathways due to imperfect refocusing pulses are analyzed. It is shown that mirror image ghosts result if the encoding RF pulse matrix is real-valued. These ghosts can be avoided as long as the rows of the RF pulse matrix are conjugate symmetric, which implies that spatial profiles are real valued. Non-Fourier encoding using bases derived from wavelet, Hadamard, and other real-valued orthogonal functions does not result in a mirror ghost artifact. A RARE sequence for non-Fourier encoding has been implemented on a clinical imaging system and successfully applied for brain imaging.