Speculative decoding (SD), where a small draft model is employed to propose *draft* tokens in advance and then the target model validates them in parallel, has emerged as a promising technique for LLM inference acceleration. Many endeavors to improve SD are to eliminate the need for a draft model and generate draft tokens in a retrieval-based manner in order to further alleviate the drafting overhead and significantly reduce the difficulty in deployment and applications. However, retrieval-based SD relies on a matching paradigm to retrieve the most relevant reference as the draft tokens, where these methods often fail to find matched and accurate draft tokens. To address this challenge, we propose *LogitSpec* to effectively expand the retrieval range and find the most relevant reference as drafts. *LogitSpec* is motivated by the observation that the logit of the last token can not only predict **the next token**, but also speculate **the next next token**. Specifically, *LogitSpec* generates draft tokens in two steps: (1) utilizing the last logit to speculate the next next token; (2) retrieving relevant reference for both the next token and the next next token. *LogitSpec* is training-free and plug-and-play, which can be easily integrated into existing LLM inference frameworks. Extensive experiments on a wide range of text generation benchmarks demonstrate that *LogitSpec* can achieve up to 2.61× speedup and 3.28 mean accepted tokens per decoding step.

Parallel Speculative Decoding (PSD) accelerates traditional Speculative Decoding (SD) by overlapping draft generation with verification. However, it remains hampered by two fundamental challenges: (1) a theoretical speedup ceiling dictated by the speed ratio between the draft and target models, and (2) high computational waste and pipeline stall due to mid-sequence token rejections of early errors. To address these limitations, we introduce Double (Double Retrieval Speculative Parallelism). By bridging the gap between SD and PSD, our framework resolves the Retrieval Precision-Efficiency Dilemma through a novel synchronous mechanism. Specifically, we enable the draft model to execute iterative retrieval speculations to break the theoretical speedup limits; to alleviate rejections without rollback, the target model performs authoritative retrieval to generate multi-token guidance. Double is entirely training-free and lossless. Extensive experiments demonstrate state-of-the-art speedup of 5.3× on LLaMA3.3-70B and 2.8× on Qwen3-32B, significantly outperforming the advanced method EAGLE-3 that requires extensive model training. Our code is available at https://github.com/Sylvan820/Double1.