Physicists often praise quantum electrodynamics (QED) as “the most precise scientific theory ever constructed”. Its calculations depend on a technique called renormalization, which was developed circa 1947 by Hans Bethe, Sin-Itiro Tomonaga, Julian Schwinger, and Richard Feynman. That technique managed to eliminate the divergent quantities that had plagued QED’s calculations in the 1930s and 1940s. Already in the late 1940s, the renormalization program found important allies, such as Wolfgang Pauli, Léon Rosenfeld, and Freeman Dyson. A new generation was educated in the United States in the early 1950s learning that QED was no longer a problem, and that they should then approach the other fundamental interactions, namely, the gravitational and nuclear ones. Following this narrative, several historians of science—Silvan Schweber, Jagdish Mehra, Alexander Rueger, among others—claimed that 1947 was a watershed in the history of QED, when the old problems were finally solved. In this talk, I discuss whether that narrative is adequate. I analyze some discontents of the renormalization program, namely, Rudolf Haag, Fritz Bopp, Irving Segal, and Arthur Wightman. They believed that the renormalization methods had questionable foundations and were, to some of them, plain nonsense. I also discuss Gunnar Källén’s position, who was a supporter of the renormalization program and, nevertheless, an opponent of Schwinger’s methods. I claim that QED was far from being considered a solved problem outside a limited circle of physicists in the 1950s, and that the standard narrative aligned perhaps too much with Schwinger’s and Feynman’s own perspectives.