In this article, we aim to address the following research question: How can a construction organization reduce and contain errors in its projects and mitigate rework and failures? We adopt an organizing sense-making perspective to acquire a sense of order of quality (e.g., rework) and to understand its relationship with safety (e.g., unsafe behavior) in construction. We undertook semistructured interviews from a range of employees involved with delivering a construction organization's projects. Also, documentary sources were accessed to supplement the rework and safety incidents that were referenced during the interviewing process. We found that the construction organization's prevailing culture focused on error prevention, which stymied its ability to learn and reduce rework in projects. The organization consciously enacted a trade-off between quality and safety. The upshot of this either/or framing of competing values was the suppression by senior management of nonconformances, which then led to deviant behavior manifesting in projects. We also revealed that safety incidents tended to arise when people engaged in unsafe behaviors while performing rework. The empirical evidence supports our call for construction organizations to engage in error management so that they can cultivate mindfulness where individuals and project teams can improvise and better handle errors, so they are not repeated.