This worked, I was using the UploadAttachments control already, but used the MoveTo object. This off course removed the files from the cotrol.
Now I've placed the UploadAttachments control inside an update panel. This works except one thing. The files are uploaded and i get the little green 'v', but the list doesn't shift to the list overview where one can delete files with the remove button.
What could be the problem?