Summary: We present here the natural extension of our Pila-Wilkie type estimates on the number of rational points of the trascendent part of a compact analytic subset of \(\mathbb F_q((1/T))^n\) to analogous subsets of \(K^n\), where \(K\) is a general local field of any characteristic. That would integrate the analogous estimate provided by R. Cluckers et al. [Forum Math. Pi 3, Article ID e5, 60 p. (2015; Zbl 1393.11032)]. We remind in the first two sections the main ideas of our construction by correcting two minor mistakes we made in [the author, J. Number Theory 154, 201–277 (2015; Zbl 1321.11067)]. We then generalize the strategy to any local field.