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The twin-bunch technique has been a subject of intense investigation due to its application in diverse fields, such as two-color free-electron lasers and beam-driven wakefield acceleration. In this paper, we investigate the generation of twin bunches (tunable in both time and energy space) via a velocity bunching (VB) scheme in a traveling wave accelerator (TWA) by varying the TWA phase across a very large range for the first time. The results of both simulations and experiments are presented. The results show that when the phase injected into the TWA tube is set to ≪-100  degrees, VB occurs in a deep overcompression mode, where the twin bunches are continuously and widely tunable under a large TWA phase acceptance. The energy and time spaces can be adjusted in the ranges [0–3] MeV and [0–6] ps, respectively, by varying the phase of the injected bunch train from -170  degrees to -120  degrees. The deep overcompression mode is a newly explored working mode for the VB scheme. Moreover, the emittance of each sub-bunch can be preserved when the strength of the long solenoid surrounding the TWA is optimized for emittance compensation, thus maintaining the high-quality beams from photoinjectors.