If memory serves me, AmEx/Starwood had a promo this year for about a month where if you were paying Federal 1040 tax you would earn double points up to 4000 additional points. Assuming you already had 12 Starwood points, and you took advantage of this offer, your Starwood balance would go to 20,000 points at a service fee cost of two and a half percent = $100.
If you then took advantage of the Brittish Airways offer for double miles from Starpoints and converted the 20,000 Starpoints you would get the 25% bump from Starwood and end up with 50,000 British Airways miles, enough for an ecomomy ticket to Europe.