Is there some way for telling the system not to keep a log of what has been erased? I don't think to delete these manually on a regular basis. When I bring up Eraser there is a list of the files I have recently erased.
Tasks can be deleted, and the log for each task can be cleared. Anything then left behind would be cleared by a free space erase. But the best way of ensuring that your erases are not logged is to use eith er Recycle Bin or context menu erasing.
If you delete to the Recycle Bin, and then erase that, even as a saved task, the Eraser log only records that the Bin has been erased, not what was in it. If you initiate a task (either direct erasing or the Recycle Bin) from the context menu, Eraser temporarily creates a task and logs it while the task is running, but holds it in RAM and does not save it and then deletes the task entry and log if the task completes successfully. The log is only saved to disk when Eraser shuts down; by that time the task entry will have been removed.
That's the good news. The bad news is that the NTFS (journalling) file system is still busy logging everything in the background. I am still trying to work out how to clear those logs ...
The file system will delete the journal in the background; no progress will be shown. NTFS has to reset the USN ID for every file on disk, so expect to wait a few hours. A log entry will be placed in the system Log though (use eventvwr.msc)