Multiple pulse repetition interval (multi-PRI) transmission is part of an adaptive signal transmission and processing algorithm being developed to aggressively combat range-velocity ambiguity in weather radars. In the past, operational use of multi-PRI pulse trains has been hampered due to the difficulty in clutter filtering. This paper presents finite impulse response clutter filter designs for multi-PRI signals with excellent magnitude and phase responses. These filters provide strong suppression for use on low-elevation scans and yield low biases of velocity estimates so that accurate velocity dealiasing is possible. Specifically, the filters are designed for use in the Terminal Doppler Weather Radar (TDWR) and are shown to meet base data bias requirements equivalent to the Federal Aviation Administration's specifications for the current TDWR clutter filters. Also an adaptive filter selection algorithm is proposed that bases its decision on clutter power estimated during an initial long-PRI surveillance scan. Simulations show that this adaptive algorithm yields satisfactory biases for reflectivity, velocity, and spectral width. Implementation of such a scheme would enable automatic elimination of anomalous propagation signals and constant adjustment to evolving ground clutter conditions, an improvement over the current TDWR clutter filtering system.