The circadian clock is an endogenous oscillator with a period of approximately 24 hours, with the central pacemaker localized in the suprachiasmatic nucleus (SCN). Jet lag occurs because the clock requires several days to entrain to a new environment. To address this, it is common practice to use bright light exposure-a potent zeitgeber-at specific times. Here, we propose an alternative approach based on a mathematical limit cycle model: reducing the amplitude of the circadian oscillator to enhance its responsiveness to timing cues. As a proof of concept, we generated a transgenic rat line expressing a dominant-negative (DN) form of BMAL1 in the nervous system to create a model with weakened circadian function. We developed an expression vector using the mouse Prion protein promoter to express a BMAL1 DN lacking the C-terminus, a region critical for CRY1 interaction. We confirmed that the behavioral rhythms of BMAL1 DN(+) Tg rats exhibited lower amplitudes compared to their DN(-) littermates under both light-dark (LD) and constant darkness (DD) conditions. Furthermore, ex vivo SCN organ cultures from BMAL1 DN(+) rats showed lower amplitude rhythms than those from controls. When exposed to bright light at ZT14 (two hours after lights-off) and released to DD, BMAL1 DN(+) rats showed a significantly greater phase response. Additionally, following an abrupt shift in the LD cycle, BMAL1 DN(+) rats required fewer days to re-entrain to the new environment. These suggest that reducing the amplitude of the circadian oscillator enhances phase responsiveness and accelerates entrainment to new light-dark cycles.