Peer-to-Peer streaming support for 3D content (i.e., P2P 3D streaming) has recently been proposed to provide affordable and real-time virtual environment (VE) content delivery. However, the generally limited client upload bandwidth requires maximal bandwidth utilization for effective streaming. This paper proposes Bandwidth-Aware Peer Selection (BAPS), a peer selection strategy that improves the bandwidth utilization for 3D streaming. BAPS avoids request contention and peer overloading as object and user densities increase, thus improving both bandwidth utilization and system scalability. We compare BAPS with strategies that select from only peers within the area of interest (AOI) as data sources and do not consider bandwidth capacity. Our evaluation shows that BAPS achieves better performance in general, and maintains a stable minimal quality of service (QoS) for streaming, which is important for commercial applications.