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Many tax regimes collect revenue just in case other governments do not. These cross-border minimum taxes are widely believed to work best when they are unavoidable. We challenge this conventional wisdom by developing a formal model of strategic interactions under a cross-border minimum tax. As the minimum tax becomes more difficult to avoid, tax havens raise their rates towards the minimum, eroding the rate at which the minimum tax collects revenue. Sometimes, an avoidable minimum tax outperforms an unavoidable one.