We report extremely sharp lines of photoluminescence (PL) and photoluminescence excitation (PLE) spectra from single three-dimensionally confined GaAs/AlAs structures grown on square mesas patterned onto a GaAs substrate. The single structures, which had a 10-nm vertical thickness and a 0.2-μm lateral width, were measured at 8 K by microphotoluminescence. At high-excitation power, the PL and PLE spectra of the single structures exhibited broad exciton peaks several meV wide. However, when the excitation power was lowered, each heavy-hole exciton peak in the PL and PLE spectra became a series of sharp lines whose widths were respectively, about 0.5 and 0.3 meV. The sharp lines of the PL spectra were probably due to the radiative recombination of excitons localized into lateral potential islands in the single structure. In the PL spectrum at a lower excitation power, a sharp line split into extremely sharp lines (≅ 0.04 meV). This fine splitting possibly represents a difference in the confinement energy of excitons localized in potential islands that have almost the same local thickness but differ in size and microstructure. From our analysis of the PLE spectra and the resonant PL spectra, we conclude that a sharp line in a PLE spectrum is not directly related to any particular sharp line of a PL spectrum. The sharp lines of the PLE spectra can be interpreted in terms of exciton absorption whose energy is determined by the locally averaged thickness of the single structure.