In the 1760s, the international debate on the solution to determining longitude at sea is at its acme. Two solutions emerge, the mechanical and the astronomical ones. The Portuguese mathematician and astronomer José Monteiro da Rocha (1734–1819) is well aware of that debate. For him, Harrison’s No. 4 marine timekeeper cannot be seen as a solution. The desirable solution could only be astronomical. In a manuscript from c. 1765, which unfortunately he fails to publish, Monteiro da Rocha is very critical (...) of Lacaille's lunar-distance method (1759) and proposes another one. In this paper, we intend to analyse Monteiro da Rocha’s criticisms and proposals, trying to understand how this manuscript fits into the international longitude debate and the Portuguese scientific scenario at the time. Concurrently, we will re-examine the classical historiography around the English vs. French priority proposal of the lunar-distance method, purging it from its mythologies to shift it towards a more open, less linear history. (shrink)