Thanks for your help, xor and Pecoflyer.

Bottom line first: I think I've discovered a new way to fix problems in Excel: simply *ask* for help and the problem goes away!

More discussion: I'd been living with or trying to fix this problem for a couple of weeks. Xor, Excel claimed I had any number of circular references. For example, if I deleted the contents of cell M8 in my example, then Excel would say I had a circular reference somewhere else, and if I deleted the contents of that cell (which was *not* a circular reference) it would claim there was a circular reference in yet a third place, and so on.

My Excel file had several sheets, so I tried copying and pasting the contents of the sheet where all the problems were alleged to have occurred into a new Excel spreadsheet, but again got the circular reference problem.

However this morning (after rebooting) when I opened the spreadsheet in response to your suggestions, the problem was gone! I have no idea what changed. I'd made a number of changes searching for the root of the problem, but - I think! - reversed them all.

So again, thanks for the help. Pecoflyer, using INDEX might be a better approach than INDIRECT - I'll look into it.