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A key index of the performance of a rule-based pro- gram used in real-time monitoring and control is its response time, defined by the longest program execution time before a fixed point of the program is reached from a start state. Previous work in computing the response-time bounds for rule-based programs effectively assumes that all rules take the same amount of firing time, It is also assumed that if two rules are enabled, then either one of them may be scheduled first for firing. These assumptions can result in loose bounds, especially in the case programmers choose to impose a priority structure on the set of rules. In this paper, we remove the uniform-firing-cost assumption and discuss how to get tighter bounds by taking rule-priority information into account. We show that the rule-suppression relation we previously introduced can be extended to incorporate rule-priority information. A bound-derivation algorithm for programs whose potential-trigger relations satisfy an acyclicity condition is presented, followed by its correctness proof and an analysis example. [ABSTRACT FROM AUTHOR]