Can you suggest alternative billing arrangements, e.g. project or value-based billing, to hourly rate billing for service-based professionals?

I've been consulting for most of my career and billing under the standard industry expectation of hourly based billing. Over the years, I've come to believe that there must be a better way to to exchange value between a client and service provider, that more closely aligns the value provided by the service provider to the value received by the client. Do any of you have use approaches or have examples of billing models like this, that have worked well for both you and your clients? P.S. - See "Breaking the Time Barrier", by Mike McDerment, for a few examples of what I'm after here.