This Article explores the problems that arise when a will fails to dispose of an individual’s entire estate, so that she dies partially testate and partially intestate. The questions then raised include (1) whether provisions contained in the will purporting to redefine the individual’s intestate heirs should supersede the statutory designations of those heirs, (2) whether inter vivos gifts to heirs should qualify as advancements on the inheritances of those heirs under conditions of partial intestacy, and, most broadly, (3) whether courts should fill in the incomplete portion of an individual’s estate plan by extrapolating from the distributive preferences set out in the fragmentary will or by independent reference to the statutory rules of intestacy. The intent of testators is bound to vary on each of these points, this Article argues. In order to account for this predictable variation, lawmakers should grant courts limited discretion to resolve each of these issues on a case-by-case basis, taking into consideration both intrinsic and extrinsic evidence. Such an approach would differentiate the rules of partial intestacy from complete intestacy, which operates according to mechanical rules. This Article suggests policy reasons for drawing that distinction. The Article supports its analysis with empirical evidence drawn from data sets of published cases, a resource not previously exploited in connection with quantitative studies of inheritance law.