Reducing the sugar in these cookies results not only in a cookie that is not as sweet, but also in a denser cookie. The reason for this is that while creaming the butter with the sugar, tiny air bubbles are incorporated into the butter as a result of the sharp sugar crystals being smashed, at high speed, through the butter. The air bubbles then expand during the baking process allowing the cookie to rise. The added baking soda does not create any additional air bubbles during the baking process; its function is to further expand the air bubbles already present in the dough.
Having the butter at room temperature (62-68 F) prior to beating in the sugar is important, because butter that is cold is hard to beat, while butter that is warmer than 68 F will have started to melt, allowing sugar crystals to move freely through the fat without generating air bubbles.
While researching the background for this post, I came across several mentions (here and here) of the idea that letting cookie dough rest overnight in the refrigerator improves the taste and texture of the final product. So I decided to give it a try and baked half the batch right after making the dough and let the other half sit in the refrigerator overnight. The overnight rest definitely improved the flavor but a couple of cookies broke apart during the baking. Will I be resting my dough routinely? I am on the fence.