No payment method offered on postage only charge

[MarkUK]

I've got a whole load of products on sale for just the price of postage. However, if the price is set to zero, when the customer "buys" it, the postage is calculated correctly (with zonal calculation), but no payment options are offered.

Inspired by the answer to another question, I set the product price not to zero but to 0.0001.  Bingo! The product still shows up with a price of 0.00 *AND* it causes the payment options to be shown!

Not really what I'd've expected.