I make a weekly backup of my operating system (XP partition) to an external
drive using Powerquest DriveImage 7. It uses "smart sector" copying (only the
sectors in use). After the 4'th backup, I delete the oldest image(etc., etc.)
Eventually the external drive becomes quite fragmented. Assuming that my
defrag programme behaves properly, do I risk compromising the integrity of
the defragmented images ?

Defragmenting won't hurt your files.

Your hard drive is like a big book.
Some pages are filled, some are not.
At the start of the book, you have an index saying this file can be found on pages 1,3,27, and 395.
When you defragment, you reorder the pages so that your index now reads that same file is on pages 1,2,3, and 4.
The file integrity remains the exact same, as said.
You're simply putting its pieces closer together for quicker/easier access.

There is no need for defragmenting a backup drive, since there is no performance issue that you are trying to improve. I would just leave it.

My experience is that drive images usually consist of very large files and take an extremely long time to defragment. This can cause performance problems on some PCs. It's best not to defragment the files unless it is done when the PC is not in use or not at all.

Thanks all for the comments and suggestions. I'll leave well enough alone and
skip defragging.