Spring reverberation is a sonically unique form of artificial reverberation, desirable as an effect distinct from that of more conventional reverberation. Recent work has introduced a parametric model of spring reverberation based on long chains of all-pass filters. Such chains can be computationally expensive. In this paper, we propose a number of modifications to these structures, via the application of multirate and multiband methods. These changes reduce the computational complexity of the structure to one third of its original cost and make the effect more suitable for real-time applications.