Lemma 5 and used it to prove their Theorem 7. They assumed that the p-values corresponding to the true null hypotheses (i.e., null p-values) are independent and uniformly distributed. However, none of them provided a formal proof of the STP of the rejection thresholds, and without the STP the optional stopping theorem (see, e.g., Karatzas and Shreve, 1991) can not be applied and the martingale based approach in Storey et al. (2004) and Liang and Nettleton (2012) fails. In this article, we introduce Storey-type FDR procedure in Section 2 as an extension of Storey’s procedure in Storey et al. (2004), introduce the concept of regular estimator of the proportion of true nulls, and show in Section 3 that the STP of the rejection threshold of a Storey-type FDR procedure is generic when the estimator of the proportion of true nulls is regular. This provides a formal justification of the use of STP of the rejection thresholds in Storey et al. (2004) and, if needed, in Chen and Doerge (2014). However, it also implies that the rejection threshold of an adaptive FDR procedure may not be a stopping time when the estimator of proportion true nulls is not regular. Further, we show that a Storey-type FDR estimator at the threshold of its corresponding Storey-type FDR procedure equals to the targeted FDR level. Some consequences of these findings are given in Section 4, which include that a Storey-type FDR procedure is always conservative when the null p-values are independent and uniformly distributed. We end the article with a short discussion in Section 5. Let there be m null hypotheses H$_{i}$ with associated p-values p$_{i}$ for i = 1 , ..., m , such that only m$_{0}$ among them are true nulls and the rest false nulls. However, the true status of each H$_{i}$ is unknown, and so is the proportion of true nulls π$_{0}$ = m$_{0}$/m . A one-step multiple testing procedure (MTP) claims that H$_{i}$ is a false null if and only if p$_{i}$ ≤ t using a rejection threshold t ∈ [0 , 1]. It gives R ( t ) as the total number of null hypotheses claimed to be false and V ( t ) as the number of true nulls claimed to be false. The FDR (Benjamini and Hochberg, 1995) of such an MTP is defined as where E is the expectation. FDR ( t ) = E [ V ( t ) / max { R ( t ) , 1 } ] , 2 2 Storey-type FDR procedures