Taken from the spine area of a deer, backstrap is arguably the tenderest cut of venison.  While it can be grilled whole, the backstrap is quite lean and will dry out quickly so I prefer to cut it into smaller fillets before quickly grilling it over direct high heat. 

To finish the fillets, I find that a compound butter comprised of toasted pecans and dried cherries is a perfect compliment to the slight gamey taste of venison.