  Ren and the second author established that the weakly optimal subvarieties
(e.g. maximal weakly special subvarieties) of a subvariety $V$ of a Shimura
variety arise in finitely many families. In this article, we refine this
theorem by (1) constructing a finite collection of algebraic families whose
fibers are precisely the weakly optimal subvarieties of $V$; (2) obtaining
effective degree bounds on the weakly optimal locus and its individual members;
(3) describing an effective procedure to determine the weakly optimal locus.
