This paper considers optimizing adjustable fractional-delay (FD) all-pass filters in the minimax sense. A filter structure proposed by Makundi, Laakso and Valimaki and referred to as an all-pass gathering structure is employed. The optimization is performed in two basic steps. First, an initial filter is generated using a simple design scheme. Second, this filter is used as a start-up solution for further optimization being carried out by an efficient constrained nonlinear optimization algorithm. An example is included for illustrating the efficiency of the proposed design scheme. In addition, the performance and the complexity of the adjustable FD all-pass filters are compared with those of the adjustable FD finite impulse-response filters implemented using the modified Farrow structure proposed by Vesma and Saramaki. This comparison shows that both the number of multipliers and the number of adders for the resulting all-pass filters are less than 50 percent compared with their optimized FIR counterparts.