Freeing Space in iOS

For anyone else in this situation, I'm posting my experience. I did install iTunes and do a backup/restore, but that didn't fix it. It did help me see that, in fact, there was a huge chuck of data marked as "other" - this is what most forum posts describe. I began deleting apps to see if I could figure out which was responsible, but nothing reduced that wasted space. Finally, I was forced to accept the unpleasant reality. Yes, you have to wipe your phone. Since I had a backup, I went to Settings -> General -> Reset (at the bottom) -> Erase All Content and Settings. After, I used iTunes to do a restore. This brought back pretty much everything the way I had it. However, apps that I deleted I had to search and reinstall from the AppStore. (Why don't they have a "my apps" list like Amazon does?)