[euromodder]

The Michelin Energy Saver and Goodyear Efficientgrip were tested to be the best tyres as far as low rolling resistance goes.
But they performed worse in overall handling.

The better handling (claimed to be !) eco-tyre - the Continental ecocontact 3 - performed better, but didn't really show better fuel economy.

If you go the LRR way, you must be prepared to give up on handling (especially in the wet) and braking performance.
This is not that much of an issue if you also adapt your driving style.