We have performed an experimental structure determination of the ordered p(sqrt[3] x sqrt[3])R30 degrees structures of chlorine and iodine on Au{111} using low-energy electron diffraction (LEED). Despite great similarities in the structure of the underlying substrate, which shows only minor deviations from the bulk positions in both cases, chlorine and iodine are found to adsorb in different adsorption sites, fcc and hcp hollow sites, respectively. The experimental Au-Cl and Au-I bond lengths of 2.56 and 2.84 A are close to the sums of the covalent radii, supporting the view that the bond is essentially covalent in nature; however, they are significantly shorter than predicted theoretically.