Converting FSA's to RE

We just finished looking at the mechanism for converting a DFSA to a RE in class. The general idea is to observe the pathways of which each state reaches and exits a particular state and formalize a statement that describes those movements. In doing this we are able to eliminate that particular state and as we repeat the process we eventually remove all the states and are left with a single expression. However, this expression tends to be incredibly complex. Although the expression works and the process is intuitive enough, i'd like to see more examples of simplifying the regular expression that emerges form the process.