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:

Ran into trouble sometime back with a tangled gradient mesh. After transforming the gradient mesh, I noticed new corners and curves without (visible) points. These apparently could not be moved or otherwise manipulated.

Found a "Gradient Mesh Kinks" thread on Adobe forums. Apparently, when a gradient mesh is transformed, invisible 'helper' points are automatically added - supposedly to help it keep its shape but they often end up doing the opposite.

Tried the first few suggestions from the forum. They may have worked for other people on the thread but none worked for me. Was about to tear my hair out with frustration when I came across calvin_rotten's comment near at the bottom of the thread. The tip about adding new anchor points set me on the right path. Anyway, although not a single thread comment taken on its own was useful to me, combining approaches from the experience of others solved the problem.

Thanks to all who shared their relevant experiences.