Defect prediction models can be beneficial to prioritize testing, analysis, or code review activities, and has been the subject of a substantial effort in academia, and some applications in industrial contexts. A necessary precondition when creating a defect prediction model is the availability of defect data from the history of projects. If this data is noisy, the resulting defect prediction model could result to be unreliable. One of the causes of noise for defect datasets is the presence of “dormant defects,” i.e., of defects discovered several releases after their introduction. This can cause a class to be labeled as defect-free while it is not, and is, therefore “snoring.” In this article, we investigate the impact of snoring on classifiers’ accuracy and the effectiveness of a possible countermeasure, i.e., dropping too recent data from a training set. We analyze the accuracy of 15 machine learning defect prediction classifiers, on data from more than 4,000 defects and 600 releases of 19 open source projects from the Apache ecosystem. Our results show that on average across projects (i) the presence of dormant defects decreases the recall of defect prediction classifiers, and (ii) removing from the training set the classes that in the last release are labeled as not defective significantly improves the accuracy of the classifiers. In summary, this article provides insights on how to create defects datasets by mitigating the negative effect of dormant defects on defect prediction.