We demonstrate efficient room-temperature photoluminescence and spectral tuning of epitaxially grown ZnSe/CdSe quantum well structures almost over the whole visible spectrum (470--600 nm wavelength). The key element to achieve the observed high quantum efficiency and enormous tuning range was the implementation of a special strain engineering technique, which allows us to suppress substantial lattice relaxation of CdSe on ZnSe. Previous studies indicated that a CdSe coverage exceeding 3 ML on ZnSe results in the formation of extensive lattice defects and complete quenching of the photoluminescence at low and room temperature. In contrast, our approach of strain engineering enables the deposition of planar CdSe quantum wells with a thickness ranging from 1 to 6 ML with excellent optical properties. We attribute the observed experimental features to a controllable strain compensation effect that is present in an alternating system of tensile and compressively strained epitaxial layers and supported this model by calculations of the transition energies of the ZnSe/CdSe quantum wells.