Removing unwanted kinks in Adobe Illustrator's gradient mesh

Here is what worked for me on Adobe CS4:

1. Select the gradient mesh
2. Select the Add Anchor Point tool. Now the invisible 'helper' points that cause the kinks will become visible.
3. Add 2 anchor points, one on either side of the 'helper' point that you want to get rid of.
4. Select the 2 points you just added. (When you use a selection tool, the 'helper' point will become invisible again. Don't worry, it's still there.)
5. Hit the Delete button. (When you delete the 2 points on either side of the helper point, the helper point will also be deleted.)
6. Now select the gradient mesh again. You will see that the kink is gone.

Background and acknowledgments: