An epi-illuminated microscope configuration for use in fluorescence correlation spectroscopy in bulk solutions has been analyzed. For determining the effective sample dimensions the spatial distribution of the molecule detection efficiency has been computed and conditions for achieving quasi-cylindrical sample shape have been derived. Model experiments on translational diffusion of rhodamine 6G have been carried out using strong focusing of the laser beam, small pinhole size and an avalanche photodiode in single photon counting mode as the detector. A considerable decrease in background light intensity and measurement time has been observed. The background light is 40 times weaker than the fluorescence signal from one molecule of Rh6G, and the correlation function with signal-to-noise ratio of 150 can be collected in 1 second. The effect of the shape of the sample volume on the autocorrelation function has been discussed.