The gas-phase conformational preferences of the model dipeptides Z-Glu-OH and Z-Arg-OH have been studied in the low-temperature environment of a supersonic jet. IR-UV ion-dip spectra obtained using the free electron laser FELIX provide conformation-specific IR spectra, which in combination with density functional theory (DFT) allow us to determine the conformational structures of the peptides. Molecular dynamics modeling using simulated annealing generates a variety of low-energy structures, for which geometry optimization and frequency calculations are then performed using the B3LYP functional with the 6-311+G(d,p) basis set. By comparing experimental and theoretical IR spectra, three conformations for Z-Glu-OH and two for Z-Arg-OH have been identified. For three of the five structures, the dispersion interaction provides an important contribution to the stabilization, emphasizing the importance of these forces in small peptides. Therefore, dispersion-corrected DFT functionals (M05-2X and B97D) have also been employed in our theoretical analysis. Second-order Møller-Plesset perturbation theory (MP2) has been used as benchmark for the relative energies of the different conformational structures. Finally, we address the ongoing debate on the gas-phase structure of arginine by elucidating whether isolated arginine is canonical, tautomeric, or zwitterionic.