Do I make federal loans private?

I am about to refinance a bunch of private and federal loans for a lower interest rate saving me about $100 a month. In the fine print before signing the loan, I noticed there was some verbiage about possibly getting a lower rate by refinancing the federal loans keeping them federal. How do i do this? The government websites I see are terrible and explain things poorly. The three federal loans are at 6.8% and I'll be lowering them to 5.99%. Should I do this and save interest but lose the benefits?