The important influence of multiple gaps in the superconductivity of MgB2 and Fe-based compounds, especially because of the possibility that manipulation of a second gap can significantly raise the upper critical field H-c2, has refocused attention on Nb3Sn because anomalies in both specific heat and point-contact tunneling studies have led to the proposal that Nb3Sn is also a two-gap superconductor. Here, we search for evidence of the second gap in a careful study of the influence of the homogenization temperature on the sample uniformity. We show that it is very difficult to fabricate samples that are both homogeneous and stoichiometric. We find so-called "second-gap" anomalies disappear only after high temperature and long-term annealing. Such a well-annealed sample shows only a strong, electron-phonon-coupled, single-gap behavior. In contrast, samples reacted and annealed at lower temperatures, as in the earlier two-gap studies, show small chemical composition variations of the A15 phase. We propose that the second gap sightings are actually due to variation of T-c within very difficult-to-fully homogenize samples. A curiosity of the A15 Nb3Sn phase is that almost any mixture of Nb and Sn tries to form a stoichiometric A15 composition, but the residue of course contains off-stoichiometric A15, Nb, and other phases when the Nb: Sn ratio departs from the true 3: 1 stoichiometry. (C) 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.