The tuning of lateral and vertical correlations in self-organized PbSe/Pb 1-xEu xTe quantum dot superlattices by changes in the spacer thicknesses is demonstrated and shown to be due to finite size effects in the dot-dot interactions. As a consequence, different dot arrangements such as vertically aligned dot columns or fcc stacking are obtained for a single material system without changes in growth conditions. The different dot superstructures are shown to exhibit a different scaling behavior of the lateral versus vertical dot separation, as well as a different evolution of dot sizes and shapes.