We consider the oblique Alfv¿n wave instability for isotropic shells of pickup ions which was introduced by Wu and Yoon. We provide some further physical insight into this instability but show that the results published to date have not been correct. Our analysis indicates that the instability disappears when the thickness of the shell in velocity space becomes comparable to the average radius of the shell. Thus the generation of these waves will not lead to a filling-in of the shell. ¿ American Geophysical Union 1993