The method of Liu and Zamick for the exclusion of spurious M1 strength
through effective operators is extended to isoscalar and isovector op
erators and applied to heavy deformed nuclei using a Woods-Saxon poten
tial plus pairing. The isoscalar orbital, strength is almost purely sp
urious and carries most of the total amount of spuriousity. The method
gives the exact summed nonspurious strength,but becomes approximate w
hen applied to single If excitations. The accuracy of this approximati
on is:studied here by comparison with exact, rotationally invariant ra
ndom-phase-approximation results. It is shown that for some residual i
nteractions the ''approximate'' results can be very, different from th
e exact ones even in the presence of relatively small changes in the B
(M1) values or close to the exact results even for large changes. Exac
t results are at present the only reliable test for the validity of ap
proximate methods for the removal of spuriousity.