Lufthansa runs it's monthly mileage bargain deals. Most deals from the US aren't too interesting since these deals only apply to Lufthansa group member redemptions and the fuel surcharges easily exceed $800 per roundtrip.
However there is one exception – LOT Polish Airlines does not charge a separate fuel surcharge.
for 30,000 miles*
instead of 60,000
from Chicago, New York – JFK
Book: 01.01.2014 – 28.03.2014
Travel: 01.01.2014 – 31.03.2014
Availability is quite good (in March) and the extra charges come to $160.
Regular fares run about $840 – so it's not a great value per mile but a good option to use your Lufthansa miles from the credit card signups to Europe.