Fiadeiro and Yeronis (1982, FY hereafter) proposed a procedure that they claimed would lead to the best reference level for computing the absolute velocities in the ocean by the inverse method as described in Wunsch (1978). According to FY, the reference level obtained by the procedure is best because the correction required of the absolute velocities at this level to satisfy a set of imposed constraints is minimum among all the possible levels. However, one likes to ask whether the velocity field resulting from this choice of reference level is necessarily the best in the sense of being closest to the true velocity field. This question was not addressed in FY, but its answer could clarify, to some extent, the perspective of their procedure in the long-pursued, controversial search for the absolute velocities in the ocean...