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For finding 2-D angles and polarizations of waves arriving at a rectangular array of crossed dipoles, the Pencil-MUSIC method can achieve the near optimum performance with much less computational burden than the MUSIC (multiple signal classification). Following an angle-only ESPRIT (estimation of signal parameters via rotational invariance techniques) method, an angle-only Pencil-MUSIC can be easily formulated which is far more accurate than the former especially in the coherent case. The angle-only Pencil-MUSIC is analyzed and compared with the original Pencil-MUSIC. The new version sacrifices the polarization estimation to achieve about 8 times more efficient computation The accuracy of the new version seems no more than 4 times worse in terms of estimation deviation.