How have you tried to write the zip files into a new zip?
You should be able to write them in exactly the same way you wrote the intial files into the zip.
If you want to get rid of an empty directory (is this what you meant?) create a File object for the directory and call it's delete() method. If the directory contains files you will need to delete them first - you can get a an array of all files using the directories File object's listFiles() method.