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Professors Mark Reutlinger and John Weaver examine the conceptual dilemma that Professor Reutlinger encountered in the course of developing the series of diagrams to illustrate the Rule Against Perpetuities described in the accompanying article. To describe it briefly (if not simply), the perpetuities period for a special or testamentary power of appointment begins when the power is created (not exercised), and it ends when the appointed interest vests. Applying the "relation back" doctrine, the appointment is treated, for perpetuities purposes, as if it were a gift by the donor, rather than the donee. Under the "second look" doctrine, however, one may take into consideration events and circumstances existing at the time of exercise in determining whether, when viewed as of the time of creation, the appointed interest violates the Rule.