In this work, we present results on the formation of vertical molecule structures formed by two vertically aligned InAs quantum dots (QD) in which a deliberate control of energy emission is achieved. The emission energy of the first layer of QD forming the molecule can be tuned by the deposition of controlled amounts of InAs at a nanohole template formed by GaAs droplet epitaxy. The QD of the second layer are formed directly on top of the buried ones by a strain-driven process. In this way, either symmetric or asymmetric vertically coupled structures can be obtained. As a characteristic when using a droplet epitaxy patterning process, the density of quantum dot molecules finally obtained is low enough (2 × 10(8) cm(-2)) to permit their integration as active elements in advanced photonic devices where spectroscopic studies at the single nanostructure level are required.