I have billed both by the hour and by the project. It's been my experience that customers are happier with project based billing instead of hourly billing.
With that in mind, I always pad the project cost by an amount I feel will cover the times when the client decides to change their mind. Further, I keep the project plan pretty simple. For example, I don't write 4 pages on how the login screen will work. Instead, It's a single bullet point: "Login Page". This allows both them and I a little flexibility.
Because I keep things simple AND I allow time for flexibility AND the clients know how much it's going to cost up front, my client's are happier and I can keep better track of my income. Also, I keep in pretty close contact with them. As long as you can keep the relationship good, you'll have a long term client.
Of course, it takes a bit of self discipline in combination with experience to know how long things take to build. Along these lines I never experiment on a client's dime. When I write the proposal, I already know what I'm going to use to get the job done and I've used those tools before. Because of this I can say with confidence that a login page will take a certain amount of time to put together.
Next, don't bite off more than you can chew. If it's a big project, break it up into smaller deliverables with their own pay schedule. That way the client (or you) can decide to walk away at any point. For example, if you think the project will take 3 months, break it up into 3 pieces. Incidentally, this helps with cash flow.
Finally, don't discount your time when getting started. That scares people.