First-principles pseudopotential density functional calculations are reported for the half-monolayer K-covered {10 (1) over bar 0}-A surface of Co. Energetic comparison between several models of K adsorption is consistent with occupation of the hollow site, as indicated by previous low energy electron diffraction results. Detailed studies of charge density redistribution upon adsorption reveal aspects of metallic and ionic bonding between adlayer and substrate, but no evidence of covalent bonding. Spin polarised calculations indicate only minimal residual minority spin on the overlayer, and notably little demagnetisation of the substrate.