Traffic studies for network planning, design, management and control, require origin-destination demand data whose acquisition is difficult and expensive. Important, but often insufficient, data is collected by counting vehicles passing at specific points of the traffic network. An application of Constraint Programming for finding the minimum number and location of count-posts at urban roundabouts so as to obtain origin-destination data at minimum cost is given. By finding interesting mathematical properties, we were able to model this problem as a constraint satisfaction problem in finite domains. Prototype implementations in ECLiPSe and clp(fd) for SICStus Prolog are discussed. This paper appears as a complement to a previous work, which is described in the Internal Report DCC-2001-2, for which programs were implemented (in C) to perform an exhaustive case analysis of hypothetical roundabouts, seeking for possible patterns for the optimal solutions for some given cost functions. It is motivated by the observation that the cost criteria should be more flexible to encompass specific features of the particular roundabout in study.