My mom's chihuahua has a very dense, thick, double coat. It's about an inch long, but he is a smooth coat. My chihuahua Sophie has a smooth, glossy coat, with less than 1/4 length fur that's very short. I notice your Taz is a blue. Most of the blue's I've either had or met have a smooth coat (if they're not suffering from hair loss). The only one I've met that isn't like that is my mom's. The brother of a blue I used to have even had a short glossy coat and he wasn't even blue, just had blue parents! (I didn't know back then that was a nono). So it might be his breeding.
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