Maybe it would help if you elaborated on the problem, because strong-willed, when coupled with logical, can be a strength, rather than a weakness. That combination of traits is a great insulation against peer pressure later. It can get exhausting explaining the logic behind all of your rules, but the payoff is that the child will often self-enforce once the logic has been accepted.
And sometimes they go overboard with the self-enforcement, like when you explain why they need to wear seat belts, and they start wearing their bike helmets for every car ride, earning you judgmental stares everywhere you go.
