Just a general note on the pullup. Most people grip the bar "wrong". There really isn't a right or wrong way to do it as long as you know what each grip does. The 'wrong' grip is when you grab the bar like you would a baseball bat with your thumb wrapping around the bar. This activates a lot of muscles in the forearm and causes you to pull more with your arms than it does your back. With the added forearm activation, your grip might fail faster. But maybe you want the forearm activation. The 'right' way to grip the bar is with your thumb and 4 fingers all on the same side of the bar. Think how a monkey hangs from a branch in the tree. This way you can grip the bar longer and really activate your back muscles because you don't have a death grip on the bar. Anyway, give it a shot on the pullups if you've been gripping the bar with your thumb wrapping around the bar. Also try it on the lat pulldown machine, as you might find yourself getting better muscle activation