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Why do some near crises tip over into full-blown crisis and others do not? This paper considers existing scholarship and identifies four key barriers to using quantitative analysis for tipping-point analyses: strategic indeterminacy; the incentives for conflict parties to avoid inefficiencies; the paucity of cases; and the availability of quality data. Due to these challenges, many do not perform well as immediate causes for crisis escalation. We also argue and demonstrate through two quantitative models of crisis escalation that some variables, particularly related to domestic politics, can do well in explaining why some disputes tip into crisis and others do not. As we illustrate with reference to the 1995–1996 Third Taiwan Straits Crisis, qualitative approaches that analyze the processes by which leaders and foreign policy institutions make decisions add needed explanatory power to purely quantitative models of the potential for near crises to tip into crisis. [ABSTRACT FROM AUTHOR]