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Thin CdTe layers embedded in ZnTe matrix grown by atomic layer epitaxy have been studied by time resolved spectroscopy and spatially resolved spectroscopy. The presence of Cd-rich dotlike islands in these CdTe nanostructures is shown by both atomic force microscopy and high resolution transmission electron microscopy. Zero-dimensional nature of excitons is shown both by the temperature dependence of the decay time and observation of sharp exciton lines in microphotoluminescence spectra. Zero-dimensional excitons probed by microphotoluminescence present a doublet structure linearly polarized along two orthogonal directions. This doublet structure is attributed to bright heavy-hole exciton states split by the local asymmetry of the localization potential. Reversible spectral shifts in the emission of some single quantum dots are observed on a time scale of hundreds of milliseconds. These small shifts can be attributed to the Stark effect caused by fluctuating electric fields and can significantly affect time-integrated transition linewidths.