Summary form only given. The existence of quantum confinement in semiconductor nanocrystals allows to regard them as nanocavities for the electronic wavefunctions. The quantization of energy levels inside such nanocrystals results in quantization of the corresponding optical transitions. In fact, the absorption and photoluminescence spectra of various semiconductor nanocrystals possess rather a molecular-like character with sharp bands whose energy can be tuned by changing the size of the nanocrystals. Here, we demonstrate experimentally, that even the energy of photons emitted from exited nanocrystals can be further quantized if the semiconductor nanocrystals are placed inside a high-quality spherical 3 D microcavity. Such a "quantum dots in photonic dot"-structure allows to control precisely the emission spectrum of quantum dots.