Spoken Dialogue Models (SDMs) typically share a speech-token space for generation and synthesis, leading to long autoregressive sequences and costly inference. Lower-rate speech tokenizers shorten sequences but may introduce compression-quality trade-offs and costly replacement without breaking this coupling. To address this limitation, we propose CoSTA, a compatibility-preserving post-hoc framework that decouples generation and synthesis token spaces while retaining the original speech tokenizer and decoder. CoSTA extends the generation token space with compressed representations via mean-initialized vocabulary extension, pronunciation adaptation, and dialogue adaptation, followed by deterministic expansion back to the original speech-token space before synthesis. On bilingual speech-dialogue benchmarks, CoSTA achieves approximately $1.7\times$ expanded speech-token generation speed, lower full-response latency, and higher throughput while preserving response quality. Analyses show more sustained interaction under limited budgets and a practical trade-off among compression, decoding efficiency, and quality. Further experiments demonstrate cross-architecture transfer and complementarity to low-rate tokenization.

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