Get a band and angle it so that it provides maximum resistance at the top of the curl when the bicep is completely shortened. By doing so, there's never a drop-off in tension and you'll stimulate more muscle growth. As a bonus, the chest pad works as your built-in counterbalance against gravity, so you're forced to stay strict.
Tension is the stimulus for growth. Muscles experience the greatest amount of tension where the resistance curve is at its peak in the concentric point of an exercise. Tension can be manipulated in order to spur new mass gains.
One way to do that is to raise the resistance curve at the point where it starts to decline so that the muscles are at a disadvantage for a longer period of time. This is where accommodating resistance comes into play, like using bands to increase the resistance where it normally would descend.