Can Acronis do this?

I don't do this but I think this should work but be sure you test it to make sure it will do what you want it to.
Try this:
Make a full backup of folder A.
Delete some files in folder A and make an incremental backup of folder A.
You should now see 2 tib files on your USB drive. One is the full, the other is the incremental based on the full.
If you restore the full only you should get all the files. If you restore referencing the incremental you will only get the files that weren't delelted and/or any files that were added since the full was made.

TI does not modify the backup it has made but saves changes in a subsequent incremental backup. I don't think you should use the Consolidation option on the backup though.

The above method will give you a history of your files and has the advantage of saving intermediate versions of files if you can pick the correct incremental to start the restore from. Be aware of one weakness in long chains of incrementals - if one incremental goes bad for any reason, all incrementals newer than it are useless. For this reason, you should make another full at a suitable interval and start the chain again.

I, don't use TI to save my data files. I don't like dumping them all into a proprietary container file and I prefer them to be saved in their native format. I use SyncBack for this but there are others like Karen's Replicator and perhaps your Cobian Backup but the choice is yours.

First of all - Thanks a lot for responding to my question!

I have tried the solution you suggest, but found it very "clumsy" and in the end, it also deletes the old backup files.

Because, as you also mention, when you do an incremental or differential backup, Acronis stores an increasing amount of backup fragments, which makes the backup increasingly fragile and confusing. Further more, if you don't want several hundreds of backup fragments, you will have to do a full backup at some point. And when you do this, Acronis deletes files that are present in the initial backup, but not in some of the backup fragments.

At least - this is my experience when I did my tests and research with the different backup solutions. Maybe I've done something wrong or misunderstood something.

I checked the backup software you mentioned, which you use. It doe's exactly what I'm looking for, which Cobian also do.

So as a conclusion, I guess that Acronis isn't capable of doing backups of new and changed files only. Does, however, have a hard time believing that could be true.

If anybody out there has a solution, please let me hear from you.

I just tried it and it does work but you have to be careful what you select when recovering the files. If you make a full, then delete a file and then make an incremental, selecting the full when doing the restore will show the later deleted file. If you select the incremental when doing the recovery, the deleted file will not be there.

I agree it is cumbersome and if you were trying to get back an old file you might be doing a fair bit of searching if the incremental chain was long but it does have the advantage of keeping the file history intact. This is something you have to be aware of in using other methods because unless you have a versioning capability, you will only have the last version of the file in the backup.

Your statement isn't correct, Acronis does do backups of new and changed files. The old ones are still there (in the chain of backups up to the point where it was deleted) and each incremental does capture the new and changed files - a deleted file is also a change.

Perhaps, somebody who does Files and Folders Data backups can provide more enlightenment. I only use TI for images of C.

try GoodSync

I use TI only for imaging. btw, I'm new to it and can't stand it! I have documented a bazillion bugs and quirks which I'm still wrestling with. imo, TI is exactly how to make software as non-intuitive as possible - to say the least.

Anyway, for file backup and sync I highly recommend GoodSync
http://www.goodsync.com/
The GUI is painless with many shortcuts to doing things. It's pretty fast, can backup to anything, easy scheduling and so far has been bug-free. You can choose either from 1-way or 2-way synch modes, with or without propagating deletions and optionally retain old versions of files. You can easily change global settings. exclusions, etc. that apply to all jobs, or individual ones. The best part is that you can quickly see, configure and test jobs without delays. And I love how the whole GUI is only 1 screen - easy and done right, period. It doesn't image but after the trial ver. I purchased it without any regrets, unlike TI, which I'm forcing myself to use so I don't feel like a total idiot for spending $ on what is probably my worst sw purchase in history. I can't even give it away because it will make me look bad and I don't need the embarrassment!

I've chosen to continue to do my system and C backups with TIA and backups of documents etc. with Cobian :)