People who are working on fulfilling some image they have of a "nice person" are usually a pain in the ass. Their efforts to be like the "nice person" they've invented in their heads almost always get in the way of actually doing what needs to be done. Most of the time I'd rather be around someone who is honestly selfish than someone who is forever trying to be selfless. The kind of forced helpfulness such people engage in is almost never helpful at all. It's annoying. Sometimes it's even harmful.
But those of us who realize that we actually aren't as good as we could be have a real dilemma. What do you do when you recognize that you really are greedy, envious, jealous, angry, pessimistic and so on and on and on?
To me, it seems like the recognition of such things is itself good enough. It's not necessary to envision a better you and try to remake yourself in that image. Just notice yourself being greedy and very simply stop being greedy. Not for all time in all cases. Just in whatever instance you discover yourself being greedy. If you're greedy on Tuesday for more ice cream, don't envision a better you somewhere down the line who is never greedy for more ice cream. Just forgo that last scoop of ice cream right now. See how much better you feel. This kind of action, when repeated enough, becomes a new habit. Problem solved.
As far as mindfulness and concentration are concerned, it works the same way. At the moment you notice yourself drifting off, come back. You might start drifting off again a nanosecond later. But that's OK. When you notice it again, come back again. Repeat as necessary.