Gary points me to this 'unannounced United award sale' that allows you to fly to Europe in business class for just 57,500 miles (one-way) instead of the usual 70,000.
Flights from the continental US to Europe are 57,500 in January, February and March 2015.
Remember that United's definition of Europe is pretty big and includes Turkey and Georgia.
The regular price is 70,000 for the one-way on partners to Europe in business class (don't fly Lufthansa in Business Class, try Turkish Airlines).
If you throw in 5,000 miles more, you can route from/to Hawaii. If you book a round-trip with United awards, you can stop-over on the West Coast.
Sometimes there is no trick required – you just need to book when the 'sale is on'.