Fluorescence correlation spectroscopy (FCS) has become an important and widely used technique for many applications in physics, chemistry, and biology. The parameter most frequently addressed by FCS is the diffusion of molecules in solution. Due to the highly non-linear connection between the diffusion coefficient and a measured autocorrelation function, it is extremely difficult to analyse the accuracy of the diffusion-coefficient determination in a FCS experiment. Here, we present a simplified analysis based on some general maximum-likelihood considerations, and numerical result are given for the dependence of the accuracy of the diffusion-coefficient determination on sample concentration, brightness, and measurement time. Optimal concentration values for performing FCS are found.