You are never leaking less than you think. There is information in the bitcoin chain. It is not likely to be useful without pairing it with other information (and there are ways to make that harder), but I'd be more than hesitant to say "useless" - and certainly leery of betting my freedom or significant amounts of my privacy on it. That said, it is clearly better against at least some threats than other available payment systems, in terms of anonymity.