In this work we present IRAM-30m telescope observations of a sample of bulge-dominated galaxies with large dust lanes, which have had a recent minor merger. We find these galaxies are very gas rich, with H2 masses between 4x10^8 and 2x10^10 Msun. We use these molecular gas masses, combined with atomic gas masses from an accompanying paper, to calculate gas-to-dust and gas-to-stellar mass ratios. The gas-to-dust ratios of our sample objects vary widely (between ~50 and 750), suggesting many objects have low gas-phase metallicities, and thus that the gas has been accreted through a recent merger with a lower mass companion. We calculate the implied minor companion masses and gas fractions, finding a median predicted stellar mass ratio of ~40:1. The minor companion likely had masses between ~10^7 - 10^10 Msun. The implied merger mass ratios are consistent with the expectation for low redshift gas-rich mergers from simulations. We then go on to present evidence that (no matter which star-formation rate indicator is used) our sample objects have very low star-formation efficiencies (star-formation rate per unit gas mass), lower even than the early-type galaxies from ATLAS3D which already show a suppression. This suggests that minor mergers can actually suppress star-formation activity. We discuss mechanisms that could cause such a suppression, include dynamical effects induced by the minor merger.