The technique of scanned-energy photoelectron diffraction has been used to obtain detailed information on the adsorption site and internal structure of propyne (CH3CCH) and 3,3,3-trifluoropropyne (CF3CCH) on Cu(111). Both molecules are bound to the surface via the acetylenic unit in a site analogous to that previously found for ethyne on Cu(111). In particular, the acetylenic unit is parallel to the surface in a cross-bridging position such that one of the C atoms is above a fcc hollow site while the other is above a hcp hollow site, giving a C-C bond length of 1.47 Angstrom. The methyl/trifluoromethyl group is strongly tilted away from the surface and is attached with equal probability to the C atoms in the fcc and hcp hollow sites. The molecular plane is perpendicular to the surface. The fluoro group of CF3CCH is preferentially oriented in the cis conformation. From the LEED pattern and the calculated coverage of 0.25 ML, a possible overlayer arrangement for propyne and 3,3,3-trifluoropropyne on Cu(111) has been proposed. For this overlayer the orientation of the F-3 group can be explained by intermolecular steric repulsion.