Fully coherent InAs quantum dots and InAs quantum dots grown on self-organized two-dimensional (2D) islands by atmospheric pressure metalorganic chemical vapor deposition are investigated. The significantly lower critical thickness window of between 1 and 2.0 monolayers for fully coherent dots is attributed to the suppression of a segregated indium floating layer. An InAs quantum dot density of 4.7×1010 cm−2 was achieved on GaAs, and a highly localized InAs quantum dot density of over 5×1012 cm−2 was achieved on 2D InAs islands.