This paper illustrates an approach to sequential hypothesis testing designed not to minimize the amount of data collected but to reduce the overall amount of processing required, while still guaranteeing pre-specified conditional probabilities of error. The approach is potentially useful when sensor data are plentiful but time and processing capability are constrained. The approach gradually reduces the number of target hypotheses under consideration as more sensor data are processed, proportionally allocating time and processing resources to the most likely target classes. The approach is demonstrated on a multi-class ladar-based target recognition problem and compared with uniform-computation tests.