As three frequently used techniques for adaptive reprogramming in the QROM, the adaptive One-Way to Hiding (O2H) proposed by Unruh (CRYPTO 2014), the GHHM adaptive reprogramming proposed by Grilo et al. (ASIACRYPT 2021), and the Pan-Zeng adaptive reprogramming proposed by Pan and Zeng (PKC 2024), address different reprogramming scenarios, and do not appear to imply one another. Nevertheless, the recent result of Jaeger (ASIACRYPT 2025) reveals a surprising connection: all of these three adaptive techniques can be implied by a non-adaptive technique called Fixed-Permutation O2H (FP-O2H), which also yields tighter bounds for Unruh’s adaptive O2H and Pan-Zeng adaptive reprogramming. In this paper, we reconsider the implication between FP-O2H and GHHM adaptive reprogramming. We first introduce a variant of FP-O2H, called the Double-Oracle-Fixed-Permutation O2H (DOFP-O2H). Then, by applying this variant, we derive a tighter bound for the GHHM adaptive reprogramming. Thereby, our result complements Jaeger’s findings by addressing the final piece, showing that the non-adaptive O2H not only implies adaptive reprogramming in the QROM, but also yields tighter bounds. In addition, a direct application of our tighter GHHM adaptive reprogramming yields a tighter EUF-CMA security proof of Fiat-Shamir transform in the QROM: the security loss with respect to the number of signing queries \(q_s\) decreases from \(O(q_s)\) to \(O(\sqrt{q_s})\) . Furthermore, we reconsider the implication between FP-O2H and the ABKM permutation resampling proposed by Alagic et al. (EUROCRYPT 2022). By applying our DOFP-O2H, we reprove the ABKM permutation resampling, and derive the same bound as that of Alagic et al. This improves Jaeger’s result, and suggests that the FP-O2H not only can be applied to analyze the reprogramming in the QROM, but also has potential for analyzing reprogramming in the random permutation setting.