Do you have some type of grips on your ruler to keep it from slipping...you know those little clean plastic dots...

I too am left handed. Generally I cut from the opposite direction of right handed persons. If you are cutting strips or squares in 1/2, 1/4" increments, try the June Taylor square cut ruler. It has slots at specific widths and the rotary cutter stays in the slots. It does require that you line the "0" line up straight on the edge of the fabric and hold it in place.
Good luck you will get there.

I really like the Martelli rotary cutter. I am right handed so I use the red one. For me it is much easier and not as tiring to cut alot of fabric. The black handled ones are for lefties! I got mine on Amazon, loved it so much I got another one to carry in my quilt bag to classes, and also the bigger one. After trying it, several members of my groups have gotten them! Good luck! Ann

You can get a ruler for left hand I am also left handed it showes you where to put the handle for left hand I line up my fabric on a line put my ruler on the fabric if I want to cut 2 " or what ever & line the ruler extending off the material on the mat & line it up then cut. it might sound hard but it isn't also you can go to your store & they will show you how . If I can help anymore let me know .

Get the slotted rulers. They are wonderful.

http://quiltbug.com/notions/rulers.htm -- scroll down the page to shape cut slotted rulers. There is even a video to watch.

My problem is not slippage, at least not so much. My problem is getting the fabric actually cut. Even with a brand new blade, even cutting single layers, I get a lot of skips, where the fabric just isn't cut. If I go back, then the 2nd cut doesn't quite line up. I have an olfa 45 ml that I use mostly. I work on either my dinner table or the kitchen counter, the height doesn't seem to make a diference. I end up either using scissors or for strips, tearing. Any advice here?

This happens to me also, but I can go back and forth in a slotted ruler to make certain all fabric is cut and it cuts on the same line.

I'm left-handed and I have no problem.
Swap the side that your blade is on. When holding my rotary cutter in my left hand, the blade is on the right side of the cutter. Hope this helps.

Also, try the stick-on sandpaper dots on the underside of your ruler. They make a HUGE difference and I'm sure you can find them at your LQS. The stick on dots at Lowes may cause problems because they are thicker and cause the ruler to raise which may, in turn cause you more problems.

If it weren't for precuts I would have quit quilting. That is until I found the June Tailor shape cut and the little sand paper dots.