That's correct, the DOL is only authorized to recover minimum wages and overtime compensation. In my experience, they will typically not push as hard to recover as much in wages as a private wage and hour attorney. The other advantage of hiring a private attorney (most of whom will work on a contingent-fee basis) is that they can go after the remaining difference between the minimum wage and your hourly pay rate. Also, bear in mind that as a private attorney, if they are successful in recovering your minimum wages, the employer will have to pay their reasonable attorney's fees. That fee-shifting provides more leverage for a higher settlement.