Light won't turn off with new dimmer switch?

I recently changed my standard light switches for dimmer switches. They are a standard twist on off switches that operate from just one switch. I followed the wiring off the previous switch where there were 2 wires going in to com and 1 wire going in to L1. However, when you switch the dimmer off the light stays on (very faintly). It is obviously still drawing a small amount current but I don't know how to fix it??