Bicycle Mechanics - Will rapidfire shifters work on my bike?

Hi, I'm new to the forums and just had a quick question.

I recently bought a Nakamura Phenom 2.1, it's completely "stock" and I was having troubles with my grip shifter on the left side (the one that controls the front derailleur). It has 3 speeds and when I turn it, it has multiple clicks between each gear unlike a rapid shifter where you push it once and it goes to the next in one fluid movement. I always find my self searching through all of the clicks on my left shifter before I find where it is suppose to be to get to the next gear correctly. I was wondering if I could swap out the left shifter to a rapidfire shifter and leave my other shifter (right one) as the grip shift.

The one that I was looking at was this one:
Shimano Alivio Rapid Fire shifters 3speed left, MTB M410
Here is the link:
http://cgi.ebay.com/Shimano-Alivio-Rapid-Fire-shifters-3sp-left-MTB-M410-/290553459811?pt=Cycling_Parts_Accessories&hash=item43a655f463&x=34&y=0#ht_2838wt_1139

If I bought this shifter, would it release me from my current problem and would it be compatible with my bike?

Thanks a ton.:)

If you will find the spot on the shifter where the cage is centered on the middle ring, and place a very small piece of tape, of a dab of touchup paint or nail polish, you will know exactly where to shift to for each of the three gears. All the way to each end for small or big and right in the middle where the mark is for the middle. The advantage of your current shifter is that you can adjust the cage position in small increments. You lose that with rapidfire or triggershifters.
The Alivio shifter will probably work with your setup, unless someone else knows otherwise. A new shifter will cost more than a dab of nail polish.

This kind of racheting shifter is similar in operation to a friction shifter, and can be useful to 'trim' the front derailleur to stop the chain rubbing. As you shift at the back, the chain will move at the front due to the change in angle, and can sometimes rub on the derailleur. Rapidfire shifters mean you can't adjust the derailleur to compensate, and this is probably a reason why non-indexed shifting is still popular for front derailleurs.

With practice, you should be able to shift 'by ear', adjusting the shifter until the rattling stops. If you can find a position where the chain clears the derailleur in all rear gears, marking it with a drop of paint as suggested will make it easier to find.