Classical coverage models, adopted for second-generation cellular systems, are not suited for planning Universal Mobile Telecommunication System (UMTS) base station (BS) location because they are only based on signal predictions and do not consider the traffic distribution, the signal quality requirements, and the power control (PC) mechanism. We propose discrete optimization models and algorithms aimed at supporting the decisions in the process of planning where to locate new BSs. These models consider the signal-to-interference ratio as quality measure and capture at different levels of detail the signal quality requirements and the specific PC mechanism of the wideband CDMA air interface. Given that these UMTS BS location models are nonpolynomial (NP)-hard, we propose two randomized greedy procedures and a tabu search algorithm for the uplink (mobile to BS) direction which is the most stringent one from the traffic point of view in the presence of balanced connections such as voice calls. The different models, which take into account installation costs, signal quality and traffic coverage, and the corresponding algorithms, are compared on families of small to large-size instances generated by using classical propagation models.