I'm sure my ukemi looks terrible, but for one forearm to the face I missed last week, I usualy can get out of harm's way and not get hurt in the fall, so I'm not too upset about mine...just lots of room to improve. My first dojo taught me to breakfall because someone had to practice the throw you describe, and wanted a light uke to do it with...it has remained my favorite fall.
I was discussing what makes ukemi fun and easy to learn the other day with someone, and I think trust has a lot to do with it. I could trust my first dojo partners to always have my safety in mind above all else (including looking good to sensei, and making something work) and so from my first roll onward I had total trust. That goes a long way to relaxing, which I think is the secret to easy ukemi; it let me just concentrate on connecting to and moving with nage, and let him decide the timing and when he saw a spot to put me, the throw.