  The standard prescription for computing Wilson loops in the AdS/CFT
correspondence in the large coupling regime and tree-level involves minimizing
the string action. In many cases the action has more than one saddle point as
in the simple example studied in this paper, where there are two 1/4 BPS string
solutions, one a minimum and the other not. Like in the case of the regular
circular loop the perturbative expansion seems to be captured by a free matrix
model. This gives enough analytic control to extrapolate from weak to strong
coupling and find both saddle points in the asymptotic expansion of the matrix
model. The calculation also suggests a new BMN-like limit for nearly BPS Wilson
loop operators.
