Exciton properties of self-organized InAs/GaAs QDs are investigated. Size-selective spectroscopy reveals the excited single-exciton transition spectrum and enhanced polar exciton-LO-phonon coupling. A good qualitative understanding of the experimental results is achieved by eight-band k Á p calculations. Renormalization of the single-exciton spectrum in highly populated QDs shows the importance of many-particle interactions in the strong confinement limit. The ground state transition energy decreases by $16 meV for QDs occupied with $18 excitons.The formation of coherently embedded nm-sized islands in Stranski-Krastanov growth has evolved as a powerful means to produce high-quality nm-scale quantum dots (QDs) with large substrate splitting [1]. The large spread of possible structural properties, the limited characterization methods, and the sophisticated numerical approaches required to predict the electronic spectrum in such strained low-dimensional structures have hampered a detailed identification of optical transitions, yet. In particular the excited state transition spectrum depends on the structural properties of the QDs [2, 3].Here we report on the electronic properties of self-organized QDs in the InAs/GaAs model material system, comparing results of high-density photoluminescence (PL) and PL excitation (PLE) spectroscopy. The results are discussed on the basis of eight-band k Á p calculations for idealized pyramidal InAs/GaAs QDs [2]. The investigated samples (dubbed S300, P300, and V300) were grown by molecular beam epitaxy on semi-insulating GaAs(001) as described in detail in Refs. [4,5]. Structural characterization yields island densities > 400 mm --2 and suggests pyramidal shapes with base lengths between $14 and $19 nm. The optical properties of the samples have been studied in detail recently [6][7][8].Two complementary methods are currently used to access the excited state transition spectrum of QDs. On one hand, state filling in PL (see, e.g. Fig. 1a) is commonly used to observe excited state transitions [9][10][11]. The inhomogeneous broadening and manyparticle effects limit, however, the value of comparisons with single-particle or singleexciton models. On the other hand, PLE experiments (see, e.g. Fig. 1b) probe size-selectively the QD absorption spectrum [12], provided intradot relaxation is faster than competing recombination processes [8]. Figure 2a shows PLE spectra of the V300 sam-1 ) Corresponding author;