I ended up rolling mine 1/4 in. thick. I wish I had seen your post before I iced them.
I looked everywhere & finally found a cookie icing recipe on Wilton's site--5 c. confectioner's sugar, 1/4 c. milk & 1/4 c. light corn syrup. Boy, did I have to thin that icing! It wouldn't even come out of the decorating bag!!! Well, anyway, it tastes okay. The No-Fail Sugar Cookies, however, I love! I really like the tip about rolling them between parchment paper--NO EXTRA FLOUR! I used 1/2 vanilla & 1/2 almond flavoring in my 1/2 batch.
I made them Thursday night & they still good now on Saturday night! Actually, I think they are better than they were the first night.
Well, thanks so much for all of your help.