One of the key problems in modern astrophysics is understanding how and why galaxies switch off their star formation, building the “red-sequence” that we observe in the local Universe. Post-starburst (“E+A”) galaxies, where a galaxy has recently undergone a massive starburst, are sufficiently common at z~1-2 that they may contribute significantly to the growth of the red-sequence at this important epoch (Wild et al. 2009). Understanding how star formation is shut off in these post-starbursts is important for understanding both their origins (e.g. gas-rich mergers or secular processes) and how rapidly, if at all, these galaxies will enter the red-sequence. We present the evolution of the molecular gas and dust properties of a sample of low-redshift post-starburst galaxies selected to span an age sequence from ongoing starburst to 1 Gyr after the starburst ended (Rowlands et al. 2015). Our results show that although a strong starburst may cause the galaxy to ultimately have a lower specific SFR and be of an earlier morphological type, multiple such episodes may be needed to complete migration of the galaxy from the blue- to red-sequence.