Summary: A method for designing minimum-phase or minimum-delay filters with an arbitrary complex transfer function inside a finite frequency interval is proposed. The method is based on a result of M. G. Krein and P. Ya. Nudel’man [Probl. Peredaci Inform. 11, No. 2, 37–60 (1975; Zbl 0328.41018)]. The filters are divided into two classes, depending on their asymptotic behaviour for high frequencies. For filters with asymptotic value different from zero, a straightforward and completely general synthesis method is proposed, yielding good numerical results. A similar method is shown to be suitable for a limited class of filters whose responses are required to approach zero in a certain sense.