I poked a big hole in my sleeping pad the one and only time I carried it outside my pack! If you do this, be sure to put it in a very sturdy stuff sack. I deflate my pad, then fold it to fit the length and width of my pack. If I need more padding I put it inside next to my back. The disadvantage of this is that it may push the heavier items away from your back, creatimg a "lever arm" on the weight (pack will feel heavier). Most of the time, I put it away from my back. The pad is light - this actually pushes the heavier items closer to my back (feels lighter when carrying). It all depends on what space is available. Sometimes I roll it up and carry it on the side (inside the pack). If you do this, be sure it is equally balanced by something light on the other side. By the way, do not put the pad inside a bear cannister when it becomes nearly empty. It will pick up food smells and you do not want to smell like a tastey meal when you are inside your tent.

The pad should not be that bulky - are you sure you are adequeately sqeezing out the air and then tightening the valve so air cannot re-enter?