Double-peaked line profiles are commonly considered a hallmark of rotating discs, with the distance between the peaks a measure of the rotation velocity. However, double-peaks can arise also from radiative transfer effects in optically thick non-rotating sources. Utilizing exact solutions of the line transfer problem we present a detailed study of line emission from geometrically thin Keplerian discs. We derive the conditions for emergence of kinematic double peaks in optically thin and thick discs, and find that it is generally impossible to disentangle the effects of kinematics and line opacity in observed double-peaked profiles. Unless supplemented by additional information, a double-peaked profile alone is not a reliable indicator of a rotating disc. In certain circumstances, triple and quadruple profiles might be better indicators of rotation in optically thick discs.