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The problem of access selection (AS) for multi-access networks has for long been addressed by both the standardization and research communities. As a result, a number of papers have proposed efficient AS algorithms that can take into account radio resource efficiency, overall capacity and quality of service (QoS) requirements in a multi-service environment. However, only a few works have developed on-line AS algorithms that do not require a priori knowledge of the traffic mix when delay sensitive (e.g. voice) and best effort (data) applications are supported. In this work, we present an online AS algorithm that performs well in a multiaccess network supporting two service classes and specifically takes into account the elastic nature of data applications. We model AS as a binpacking problem and realize that the problem is NP-complete. Therefore, we develop a heuristic algorithm called LessDamage that calculates a damage parameter and uses it as a metric for the allocation strategy. Simulation results show that LessDamage performs better in terms of blocking probability and elastic data throughput than available online binpacking heuristics, independently of the number of the available access technologies.