Position your feet and body properly before you attempt the shot. If you shoot right handed the left side of your body should be towards the target, weight on the balls of your feet. Practice your stancee and body pivot every chance you get with dry firing. Swing the horizontal cross hair through the center of the deer's body, squeeze off your shot when the lead looks right, and be sure to keep swinging, —follow through during and after the shot. Shot placement is critical for quick kills. I prefer a  250-yd zero for most 243 Winchester loads. 

Keep this lead information in your head and practice visualization leads in your own mind and with your rifle, squeezing the trigger and following through! It works for me and it will for you, too! Visualizing in your mind the various combination of shots and angles—conditions your brain's reflex habits and will make a huge difference in your shooting abilities on running game. I no longer claim to be a sharpshooter as I have a lot of shooting handicaps these days.
This 6mm Sierra 85 grain HPBT bullet was rated as a number one quick kill whitetail deer -- cartridge bullet combination! However, it is NOT my favorite 6mm .243 Win or 243/06 deer bullet & load.

Wind drift: A  45-degree wind drift angle isn't half the wind drift of a 90º-angle, but is three-quarters the drift. It has a 70 to 75 percent effect, even though the angle is only halfway between no drift effect and full drift effect. The drift effect is not proportional, due to the aerodynamic ballistics of a bullet in flight. Just remember that halfway between full and zero effect is nearly three-quarters the drift of 90-degrees.  Memorize these aerodynamic ballistic realities.

Whisky Chamberlain of Idaho took 15 consecutive big bull elk, all one shot kills, with a regular .243 Winchester, therefore I believe with the right bullet and will placed and proper ranged shots the .243/06 Wildcat ought to be adequate on elk. I don't want to buy a new larger caliber rifle just to go elk hunting once or twice.

Today, 03/04/07, I saw on the Men's Channel "American Trophy Hunters,"  - Dish-TV CH 218, a massive old Elk shot at over 200-yards & dropped in his tracks with a .243-Winchester with open iron sights. They did not mention the  bullet weight or construction type, however, it proved to me that a Well Placed .243 bullet at 200-yards will deck the biggest Elk that walks.

Therefore, my 243/06 Wildcat ought to do the job on big Whitetails, big Mule Deer and on Elk with the Grand Slam bullet. I do not want to buy another larger caliber rifle to hunt elk, perhaps once in my lifetime.

In the 243 Winchester for big Mule deer & Elk, I would use the 100-grain Remington Core-Lokt Ultra factory cartidges, if reloading I would use the 100-grain Speer Grand Slam Bullets.

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trs6mm post on the Hoadloaders Bench
 http://www.handloadersbench.com/forum23/1279.html:
I have also been rather successful with an 85 Grain BarnesX with 46.5 grains of the same powder.  This year I tried something new again for deer season, which consisted of an 85 grain Speer boattail with 46grains of 4831 again and increased my group up to about 7/8 of an inch.

I have hunted with guys in the past who love their "big" magnums and actually talked me into buying a .338 Winchester Mag. They refer to my 6MM as a BB gun.  Imagine their heads turning and their attitudes being turned when I took this muley on Public Property at 375 yards with about a 15 MPH crosswind.