It has been a challenge to accurately extract dynamic information from experimental fluorescence correlation spectroscopy (FCS) data. In this paper, we compare three major fitting methods: the model-dependent multiple exponential function (MultiExp), the empirical stretched exponential function (StreExp), and the exponential function based on the model-free maximumentropy method (MemExp). MultiExp has straight forward physical significance but it is difficult to implement and interpret in a complex system. StreExp has simple form and is easy to use but its physical picture is obscure. MultiExp is model free but its results are sensitive to experimental noise. A od choice seems to be a combination of MemExp and MultiExp. In our example, we have unraveled that two independent processes exist in the intra-chain collision of a single-stranded DNA when base pair formation is possible, which has not been observed by previous investigators. MemExp is recommended for the FCS data analysis, although caution should be exercised in the practice.