Be mindful of what you tell them to do
A strong willed child will challenge you quite often. This can be outright defiance to simply ignoring what you told them. Therefore if you say things you want them to do or not do haphazardly, you're setting up potentially unnecessary conflicts or easy chances for them to defy you unchallenged.
You must stick to you word
For bad or good, you must stick to what you said you would do. If you tell them they will lose TV privileges if they don't finish their dinner, then you have to follow through if they don't. If you don't, they will remember. Even if the consequences for them defying you isn't immediate, they still need to be carried. Never forget how smart children really are. They pick up on your behavior as much, or more so, than you do theirs. So if they see that they escaped punishment because it too long afterward, you can expect them to hope for delayed discipline in the future. This also works on the flip side. If you say that if they do a certain thing, that you'll do this for them, you MUST do it. Because if you don't stick to your word, they'll lose respect for you, which will encourage them to challenge your authority as a parent.
Only give discipline warnings that you're willing to do
While it might be tempting to throw out a very stiff punishment right away when a child is defying you, you will paint yourself into a corner if you're not truly willing to do what you said. And if you think a strong willed child won't call your bluff, you'll be in for a rude awakening. They will, constantly. And if you don't to your guns, as mentioned above, you will have undermined your own authority.
Find what can be used as leverage
I know that may sound manipulative or horrible, but in any relationship where one wields authority and the other is supposed to yield to that authority, the person in charge needs to have leverage of some sort. An employer has leverage over their employees since they can choose to terminate an employee who's insubordinate. It's the same thing with children, especially a strong willed child who will challenge your authority constantly. You need to know what things they'll find important enough so that they'll think twice about their behavior if access to those things is put into jeopardy.
Full disclosure: I support spanking (when done right,of course). The threat of force, while perhaps distasteful from an adult social perspective, is a very instinctive, visceral feeling that children will want to avoid. (This doesn't mean I advocate beating one's children, but spanking can be done effectively without causing any psychological damage). However, spanking is also leverage that you won't be able to use all the time. You definitely will want other avenues of leverage. For example, my stepdaughter loves her television shows. Promising to take that privilege away when she misbehaves has proven quite effective at times.
Now some may also encourage positive reinforcement over negative reinforcement. I would encourage caution in this realm because if a child is misbehaving, you should not offer something positive for them to stop the behavior as all this will do is encourage them to misbehave if they know they will get something nice out of it. Positive reinforcement should be used proactively to encourage new or better behavior, but never to stop bad behavior. Doing so will not only undermine your authority, but your smart strong willed child will figure out that they have leverage on you since you'll give them whatever they want (or close to it) when they misbehave.
Your authority is earned, not automatic
A strong willed child, just by their nature, is challenging your authority. And ultimately that means someone will win: either you or them. Therefore, if you want to maintain your authority, you have to earn it in their eyes. Look at this way, there's place of authority and someone has to fill it. If you don't fill it, the strong willed child will in your place.
Every conflict will gain or lose you respect
This doesn't mean the child is going to like you. That's different. But every conflict, even the small ones, will either increase or decrease their respect for you. Letting the child continue their behavior unchallenged will lose you respect. Establishing, and administering, what is acceptable and what isn't will actually gain you respect.
The more respect you've earned, the easier it can be
As you gain respect, a strong willed child will be more inclined to listen because you've "earned" it from them, so to speak. Of course, that can always be dashed if you don't stick to your guns. But, from what I've experience, it does indeed get better.
Overall, it's been a pleasure taking part in raising my stepdaughter this past year. And I look forward to the gift in her God has given me in allowing me to shape her life to walk in Him.