Do you have a short period of time in your relative's life that you know where they were but have not investigated because "it probably won't tell you anything?"
Take a look at those time periods. One of my ancestral families spent about five years in Kentucky after immigrating from Germany only to leave for Illinois where they permanently settled. Records on them in Kentucky provided several key details about their relationships and life that were not answered in records in Illinois or Germany.
Those little gaps of time may be crucial.