Government competence in delivering outcomes is often regarded as foundational to political trust. However, in this article, a different competence dynamic is proposed; specifically, whether political trust is related to government efficiency in achieving promised policy objectives. This article argues that when policy objectives are polarizing, the effect of efficiency on political trust is conditional on whether individuals support or oppose the objective. Using the case of Brexit, where the promised policy objective of leaving the European Union was polarizing, it is hypothesized that Leave voters relative to Remain voters became more trusting in cases of efficiency and less trusting in cases of inefficiency. The predictions are supported through a difference-in-differences analysis of unique real-world data over time from the British Election Study. The findings have important implications for our understanding of Brexit and also inform how political trust relates to government competence in the case of polarizing political issues.