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This paper presents a shaper architecture that scales to a large number of connections with diverse burstiness and bandwidth parameters. The architecture arbitrates fairly between connections with conforming cells by carefully integrating leaky-bucket traffic shaping with rate-based scheduling algorithms. Through a careful combination of per-connection queueing and approximate sorting, the shaper performs a small, bounded number of operations in response to each arrival and departure, independent of the number of connections and cells. To handle a wider range of rate parameters, a hierarchical arbitration scheme can reduce the implementation overheads and the interference between competing connections. Simulation experiments demonstrate that the architecture limits shaping delay and traffic distortions, even under heavy congestion.