I've heard that training them to be submissive before eating helps. You make them sit while you are preparing their bowl. After you place the bowl on the floor they can't eat until you give the release command. If they start for the bowl before you say ok, you pick up the bowl, and say, "sit." Do this until they obey. Green beans are a better diet food than carrots. Carrots actually have a great deal of sugar and if your familiar with the glycemic index, aren't really recommended because they can increase the appetite. Green beans on the other hand will help curb the appetite and make you feel full. The vet recommended replacing some of Joey's food with green beans; and now, he is finally at a healthy weight. Here's some information on the glycemic index:
The Glycemic Index