Jump tables are a common source of indirect jumps in binary code. Resolving these indirect jumps is critical for constructing a complete control-flow graph, which is an essential first step for most applications involving binaries, including binary hardening and instrumentation, binary analysis and fuzzing for vulnerability discovery, malware analysis and reverse engineering. Existing techniques for jump table analysis generally prioritize performance over soundness. While lack of soundness may be acceptable for applications such as decompilation, it can cause unpredictable runtime failures in binary instrumentation applications. We therefore present SJA, a new jump table analysis technique in this paper that is sound and scalable. Our analysis uses a novel abstract domain to systematically track the "structure" of computed code pointers without relying on syntactic pattern-matching that is common in previous works. In addition, we present a bounds analysis that efficiently and losslessly reasons about equality and inequality relations that arise in the context of jump tables. As a result, our system reduces miss rate by 35× over the next best technique. When evaluated on error rate based on F1-score, our technique outperforms the best previous techniques by 3×.