Copernicus' complex Mercury model in De revolutionibus is virtually identical, geometrically, to Ibn al-Šāṭir's (ca. 1305 – ca. 1375). However, the model in his earlier Commentariolus is different and in many ways unworkable. This has led some to claim that the younger Copernicus did not understand his predecessor's model; others have maintained that Copernicus was working totally independently of Ibn al-Šāṭir. We argue that Copernicus did have Ibn al-Šāṭir's models but needed to modify them to conform to a “quasi-homocentricity” in the Commentariolus. This modification, and the move from a geocentric to heliocentric cosmology, was facilitated by the “heliocentric bias” of Ibn al-Šāṭir's models, in which the Earth was the actual center of mean motion, in contrast to Ptolemy and most Islamicate astronomers. We show that: 1) Ibn al-Šāṭir sought to reproduce Ptolemy's critical elongation at the trines(±120°), but changed the Ptolemaic values at 0, ±90, and 180°; 2) in the Commentariolus, Copernicus does not try to produce viable elongations for Mercury; and 3) by the time of writing De revolutionibus, Copernicus is in full control of the Mercury model and is able to faithfully reproduce Ptolemy's elongations at all critical points. We also argue that claims regarding “natural” solutions undermining transmission are belied by historical evidence.