  With recent observational advancements, substantial amounts of photometric
and spectroscopic eclipsing binary data have been acquired. As part of an
ongoing effort to assemble a reliable pipeline for fully automatic data
analysis, we put Powell's direction set method to the test. The method does not
depend on numerical derivatives, only on function evaluations, and as such it
cannot diverge. Compared to differential corrections (DC) and Nelder & Mead's
downhill simplex (NMS) method, Powell's method proves to be more efficient in
terms of solution determination and the required number of iterations. However,
its application is still not optimal in terms of time cost. Causes for this
deficiency are identified and two steps toward the solution are proposed:
non-ortogonality of the parameter set should be removed and better initial
directions should be determined before the minimization is initiated. Once
these setbacks are worked out, Powell's method will probably replace DC and NMS
as the default minimizing algorithm in PHOEBE modeling package.
