The self-assembly of iron dots on the insulating surface of NaCl(001) is investigated experimentally and theoretically. Under proper growth conditions, nanometer-scale magnetic iron dots with remarkably narrow size distributions can be achieved in the absence of a wetting layer. Furthermore, both the vertical and lateral sizes of the dots can be tuned with the iron dosage without introducing apparent size broadening, even though the clustering is clearly in the strong coarsening regime. These observations are interpreted using a phenomenological mean-field theory, in which a coverage-dependent optimal dot size is selected by strain-mediated dot-dot interactions.