File>Close (shortcut: C+w) closes the current buffer. If it has unsaved changes, jEdit will ask if they should be saved first.

File>Close All (shortcut: C+e C+w) closes all buffers. If any buffers have unsaved changes, they will be listed in a dialog box where they can be saved or discarded. In the dialog box, multiple buffers to operate on at once can be selected by clicking on them in the list while holding down Control. After all buffers have been closed, a new untitled buffer is opened.

File>Exit (shortcut: C+q) will completely exit jEdit, prompting if unsaved buffers should be saved first.