We present photoluminescence studies of highly excited single self-assembled CdTe quantum dots under continuous-wave and pulsed excitations. We observe appearance of emission bands related to sequential filling of s-, p- and d-shells. We analyze the inter-shell splitting for five samples, in which the dots were formed from a strained CdTe layer of different width. We find that by increasing the CdTe layer width, the inter-shell splitting increases. In a time resolved measurement, we observe a radiative cascade between transitions involving one, two, and more than two excitons. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3643476]