I wanted to post the gravel-hoppers first, so I could explain that I found this tiny desert mantid nymph while I was struggling to take a picture of one of those pesky little grasshoppers.
Can you see him here, in the lower left of the photo?
He was tiny, about the size of a typical hatchling mantid, and fast.
This is another shot of the flying mantid I caught at the window on our first night in the desert. I saved him until the next day so I could photograph him in better light. He was also very fast. I could barely get him to hold still. I think he is the adult form of the tiny nymph. I'm not sure what kind it is. It's not a minor ground mantid, Litaneutria minor, because they have pointy eyes and this one doesn't. It might be some other ground mantid species. I showed this picture to a park ranger, but she was pretty clueless. She did say that many (or was it most) of the desert insect species are "undocumented."