I'm not a Capability Maturity Model (CMM) expert, nor do I have a bias against it, other than my tendency to be...
skeptical of all processes/methodologies that have been institutionalized. That said, I think the best way to introduce a new way of managing projects is the same no matter what process or methodology you plan on promoting.
First, pick a few of the fundamental ideas behind the process and decide to try them out. Focus on the ideas that have potential for solving painful problems and that don't require huge changes. Large ships are steered with small movements of the rudder, and so are projects. They can be changed dramatically with small, subtle changes.
Next, use those ideas to make your projects more successful without telling anyone what you're doing. Let the results speak for themselves. Discard ideas that don't work and move on to something else.
Eventually, project success will get noticed by others and they will want to know your secret. That's when you tell them the truth, that you've been experimenting with aspects of CMM, agile, or whatever. They will probably ask if there are other aspects of the approach you can use to make the projects even more successful. If they do, it's your opportunity to introduce more ideas from the methodology or to start using it more formally.
The key is to continually find ways to make your projects more successful. That is the best way to drive adoption of any new idea, whether it's your own or somebody else's.
I once used this approach to very stealthily introduce agile into a large organization. When I started, I didn't believe I would ever be allowed to use it on a large scale. In the end, however, it became the preferred approach of my group as well as several others because people could tell that the approach we used was helping us to be more effective.
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