This year I had shot a couple yearlings as a part of a management hunt (it was a "kill em' all" hunt in an urban area). So last night I decided to grill up one of the backstraps (two pieces, each about 7" long and 3" thick).

The only prep I did was thaw and refrigerate for two days, drying them off once a day.
As I got the grill heated up I salt and peppered the backstraps. I also soaked a handful of hickory chips in water.
I let the grill get up to 450 degrees I put the chips on the coals and gave it a few minutes to start smoking.
With the grate about 4" from the coals, I put the backstraps on for 3 minutes.
After 3 minutes, I gave them a quarter turn (for pretty grill marks) and left them on for another 2 minutes.
Then I flipped them over and left them on one side for another 5 minutes.
I removed them from direct heat and move them to the side of the grill while I got the table ready - probably 5 minutes.
I let them rest for 5 minutes and sliced into 1/4" medallions. They were a perfect medium rare (maybe slightly more emphasis on the rare side).

Those yearling backstraps were so tender they started coming apart as I was slicing them! After they were sliced no knife was needed, simply cut with the edge of the fork.

Moist, tender, unadulterated. My wife and kids loved it. For those out there that have always marinaded the backstraps try it without for a change.

As far as care for the deer, we skinned and deboned the deer the same day it was shot - it went from woods to cooler (packed in ice) in about 5 hours. I don't buy into the "let them hang" argument unless you have a walk-in cooler that would allow you to do it properly.