I have thundershirts for both of my girls. They do seem calmer when I get them on before the storms start, though mine are more of the "bark at the thunder and lightning flashes" type than shaking out of fear when it comes to storms. I don't have any experience with the anxiety wrap, but I have heard that often dogs who don't respond to the thundershirt do to the anxiety wrap. They both have money back guarantees, so I always tell people considering them you have nothing to lose.
