The best way to clean white leather purse?

Let me just say for the record, I love that knowledge is at your fingertips on the internet. Searching for advice on how to clean my white leather bag, that had become grimy as a result of nyc subway travel, I came across this post on Yahoo Answers: The best way to clean white leather purse?

Best Answer - Chosen by Voters

Use Mr. Clean magic eraser and water. It is VERY effective and will not hurt the leather as the eraser is not truly wet. Wipe any moisture dry from your bag and then treat with a leather conditioner to avoid cracking and hardening. Allow conditioner to dry thoroughly. -Kanakale

Can I just say - brilliant! Using the Mr. Clean magic eraser is something I would never have thought
of, but it worked exceedingly well.

Here are my results:
First photo - top of the bag still dirty, bottom of the bag Mr. Cleaned.














Halfway
Bottom of the bag - you can see the dirt line between cleaned and not clean.








Bottom of the bag fully cleaned - no more dirt