I changed my putting grip and reduced the amount of three-putts per round. I looked at the number of putts, and kept in mind the short putts under pressure that dropped. In 2012, I can recall numerous rounds without a three-putt.
I have given many putting lessons and discussed every type of grip. Aside from a short bout with a long putter I have never made a dramatic change to my putting grip. So in 2012, I changed to a cross-handed style. My new grip positions the left hand low and the right hand high. For me, the right hand settles more securely on the putter and gives me a better sense of connection to the putter head. The overall position forces the body to tilt more toward the target line. This repositioning compliments an open stance and squares the upper body. It also helps alignment for shorter putts by aligning the shoulders more parallel to the ground.
Because it is different, and the dominant hand is now at the top of the grip, essentially a weaker position, the sensation is a lack of feel. Initially longer putts are tougher to gauge. There might be an up side to this lack of feel by simply creating a softer impact on the ball. A cross-handed grip provides for better alignment, but the lack of feel results in a loss of power. Think about a baseball player hitting a bunt. He places his hand further toward the middle of the bat giving it stability. There is very little "swing" during a bunt. So the stability gives the batter control by leveraging the bat closer to the middle. This analogy is akin to a conventional putting grip. In my case it would be my old grip, left hand high. My right hand would be further down the shaft adding stability to the back of the putter (shaft). With stability lower on the shaft the impact is more solid.
Considering my tendency to hit mid and long putts too hard, I do not need more solid impact. This does not diminish the importance of striking the ball in the middle of the putter's face. It is the difference between hitting a ball with a 2x4 versus a 1x2.
Also the distance from my dominant (right) hand to the putter head has increased with the new cross-handed grip. This in turn increases the overall distance from my right shoulder to the putter head. The increased length, acting like a lever, creates a small amount of additional lag in the putter head. Although tough to see and feel, there is lag and release in a proper putting stroke. The lag creates a softer feel during impact. A small amount of give or shock absorption in the hands. I think it depends on the individual and their tendencies. If someone generally needs to hit putts softer, increasing this length will increase the lag, thus softening the impact on the ball.
There are many benefits to a cross-handed putting grip. Much of them outweigh the downside. And if you have similar tendencies as me, that is to say you would like to make more short putts and you often hit your longer putts well beyond the hole, there may be no downside. Enjoy making more putts!