Thanks, folks. There is some very useful info here. ^

Air Miles redemptions are looking more interesting, especially as I'm sitting on a pile from a useful 2x Tesco conversion a while ago. I didn't know about the £30 surcharge for non-earning accounts. Shouldn't they have told me? Perhaps if I convert one of my 18-month old Tesco vouchers, that will count?

An update on business and first class Air Miles redemptions outside Europe:

I've found that BA Club World tickets come at 3x economy, e.g. LHR-YVR = 3x 8,000 = 24,000 Air Miles. They book into I, presumably earning tier points and miles.

Similarly, F tickets come at 4x economy, e.g. LHR-YVR at 32,000 Air Miles, booking into A, again presumably earning TPs and miles.

New York is 5,000 in economy and 15,000 in biz. I couldn't find F for my dates. AA and DL flights are sometimes available for New York.

As always, YMMV - I haven't checked all destinations! - but it seems to me that if you have a bundle of Air Miles and need a few tier points or BA Miles, a look at F redemptions could be interesting.

Back to my original question, I think I'll be using Air Miles to book BD flights. And perhaps start using my Air Miles Amex regularly?