Service composition is a widely used method in ubiquitous computing that enables accomplishing complex tasks required by users based on elementary (hardware and software) services available in ubiquitous environments. To ensure that users experience the best Quality of Service (QoS) with respect to their quality needs, service composition has to be QoS-aware. Establishing QoS-aware service compositions entails efficient service selection taking into account the QoS requirements of users. A challenging issue towards this purpose is to consider service selection under global QoS requirements (i.e., requirements imposed by the user on the whole task), which is of high computational cost. This challenge is even more relevant when we consider the dynamics, limited computational resources and timeliness constraints of ubiquitous environments. To cope with the above challenge, we present QASSA, an efficient service selection algorithm that provides the appropriate ground for QoS-aware service composition in ubiquitous environments. QASSA formulates service selection under global QoS requirements as a set-based optimisation problem, and solves this problem by combining local and global selection techniques. In particular, it introduces a novel way of using clustering techniques to enable fine-grained management of trade-offs between QoS objectives. QASSA further considers: (i) dependencies between services, (ii) adaptation at run-time, and (iii) both centralised and distributed design fashions. Results of experimental studies performed using real QoS data are presented to illustrate the timeliness and optimality of QASSA.