Asian long-term contracts for liquefied natural gas (LNG) are generally thought to index LNG prices to oil prices. This should mean that LNG and oil prices are cointegrated. However, statistical evidence for cointegration using Japanese data is not strong. To resolve this puzzle, I examine 16 Japanese, South Korean, Taiwanese, and Spanish LNG import price series and allow for multiple, unknown structural breaks in the relationship to oil prices. This resolves the puzzle, and I provide estimates for the timing of breaks and the underlying average pricing terms. I relate these to count, volume, and duration data on long-term contracts and discuss how to interpret econometric estimates in light of contract data. This paper complements existing work on global gas market integration, which largely ignores how discrete changes in oil-indexed long-term contracts will affect empirical relationships.