Most of the contributions to the optimal tax-enforcement literature assume that audits are perfect and always discover evaders. However, evasion often remains undetected. To reduce the probability of such a failure, governments invest resources to improve their tax administrations' detection technology. We incorporate these kind of investments into a model that studies optimal fiscal policies under uncertain detection of evaders. We characterize their level and we show numerically how they interact with the other dimensions of an optimal fiscal policy. Finally, we highlight the differences between our results and those obtained in a model without investment in audit technology.