& following that Break will become a single Section. If you delete the Section Break that layout change cannot be maintained because the Sections preceding However, Section Breaks frequently are used to enable layout changes (e.g., the number/width of columns or the size of margins) from one Section to the next. Nature of the current Section can be changed. Section Breaks cannot be deleted from within that dialog. Contrary to what Phillip suggested, double-clcking a Section Break will not select it - It opens the Document dialog as you've discovered.
