What most managers and bean counters tend to forget is, that the gain on CI might be substantial when you look at the cumulative effect of the whole fleet vs. one year of ops. However a badly executed descent and approach uses up much more fuel than any small gain enroute, if we consider just a single flight. Now looking at the rate of pilots trained in rush-syllabi and then the performance of such pilots enroute (mind you, i am not talking about safety, but skills that lead to more economy), there might be food for thought.
Another thing that impairs any CI gain, is the tendency of cheating-scheduling close and often even over the duty limits. Just to be able to roster single crew. What i have experienced there, is that almost all pilots looking at a cheating flightplan just increase the speed in anger.
I agree with the many posters who say that flying .84 is optimal. Faster burns definitely more, slower adds up to nothing. If companies are really serious about fuel conservation, they will have to integrate us pilots much more. Training needs to be adapted, just as sops. Pilots need to be motivated to save fuel and not simply forced to fly speeds and procedures that are set up by bean counters and any pilots knows they result in peanuts. You can motivate us in many different ways, gain participation is a magic word, but most certainly some fair and credible scheduling/rostering would be a start.