Masking is a countermeasure that can be incorporated to software and hardware implementations of block ciphers to provably secure them against side-channel attacks. The security of masking can be proven in different types of threat models. In this paper, we are interested in directly proving the security in the most realistic threat model, the so-called noisy leakage adversary, that captures well how real-world sidechannel adversaries operate. Direct proofs in this leakage model have been established by Prouff & Rivain at Eurocrypt 2013, Dziembowski et al. at Eurocrypt 2015, and Prest et al. at Crypto 2019. These proofs are complementary to each other, in the sense that the weaknesses of one proof are fixed in at least one of the others, and conversely. These weaknesses concerned in particular the strong requirements on the noise level and the security parameter to get meaningful security bounds, and some requirements on the type of adversary covered by the proof-i.e., chosen or random plaintexts. This suggested that the drawbacks of each security bound could actually be proof artifacts. In this paper, we solve these issues, by revisiting Prouff & Rivain's approach.