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The problem of generating the sequence of tests required to reach a diagnostic conclusion with minimum average cost, which is also known as a test-sequencing problem, is considered. The traditional test-sequencing problem is generalized here to include asymmetrical tests. In general, the next test to execute depends on the results of previous tests. Hence, the test-sequencing problem can naturally be formulated as an optimal binary AND/OR decision tree construction problem, whose solution is known to be NP-hard. Our approach is based on integrating concepts from one-step look-ahead heuristic algorithms and basic ideas of Huffman coding to construct an AND/OR decision tree bottom-up as opposed to heuristics proposed in the literature that construct the AND/OR trees top-down. The performance of the algorithm is demonstrated on numerous test cases, with various properties.