I'm going to start with an assumption: You don't practice your short game three or four times a week. If I'm right, then you need a greenside shot that doesn't require much maintenance. You need the bump-and-run. Why? It takes very little effort to hit the ball solidly with this shot, and because it rolls most of the way, controlling distance is easy. Sure, there are places where you can't play a running shot, but you'd be surprised how often you can.
Let's start with club selection. Put your wedge away, and go with a less-lofted club. A 7-iron works great for longer shots, but a 9-iron is better inside 10 yards. Address the ball in the middle of your stance, with your weight favoring your front foot and your hips and feet open (angled well left of the target). Keep your shoulders square.
The swing should look and feel like a pendulum (above). The pivoting of your body back and through, not your hands and arms, controls the club's movement. A good thought is to keep your left arm close to your rib cage as you swing. Focus on making a slight downward hit. The ball will pop off the face and get rolling to the hole fast.