Five stationary points on the potential energy hypersurfaces for the C2H2Cl+ and C2H2Br+ cations are found at various levels of ab initio quantum-mechanical theory. At lower levels of theory, the vinyl-like cations are minima on the potential energy surface. Upon improvement of the wave function to include polarization functions and electron correlation, the structures corresponding to the classical 2-halovinyl cations become shallow minima or transition states. It is clear that both the halogen-bridged structure and the H2CCX+ isomer are stable minima that are lower in energy than HCCHX+, a fact not evident from low-level theory. This emphasizes that comparisons made between unsophisticated ab initio studies and experimental solution chemistry should be made with caution. Stabilization energies are evaluated for comparison with previous studies.