Softer Mozz

So I've made several batches of Mozz from milk and they have all turned out great (well, except for the very first time, I think the milk was too processed). Anyway, after heating and working it smooth, I chill it and then usually mix up a salad of tomatoes, basil, roasted peppers and olive oil. So good with homemade bread.

Still, the mozz comes out pretty firm. I've had fresh mozz that is very moist and delicate. I don't know how to make it to that point. I know kneading and heating releases more whey and that makes it drier. Yet, if you don't knead well, it remains grainy. Is there a trick to get a smooth cheese that has a softer texture and higher moisture content?

I think one of the keys is not letting it sit as long in the whey before you remove the curds. I cut my rest period in half and my cheese was substantially creamier. That being said it is still too firm, so hopefully some has some better ideas.