We combine ab initio density functional theory with transport calculations to provide a microscopic basis for distinguishing between `good' and `poor' metal contacts to nanotubes. Comparing Ti and Pd as examples of different contact metals, we trace back the observed superiority of Pd to the nature of the metal-nanotube hybridization. Based on large scale Landauer transport calculations, we suggest that the `optimum' metal-nanotube contact combines a weak hybridization with a large contact length between the metal and the nanotube.