What size tank do you have?
the first one looks to me like an adult Red coris wrasse,
Coris gaimard. That is not a fish I would put in a reef tank. They will flip over rocks in search for any mobile invert. So while corals may be safe, they're rather destructive and you couldnt keep crabs/snails/shrimp with any confidence.
The second one still doesnt look like the more commonly referred to christmas wrasse, but instead a rainbow or five-stripe wrasse (
Thalassoma quinquevittatum). I'm not certain about that fish and it's compatibility with reefs.
The true christmas wrasse, or ornate wrrase, is the
Halichoeres ornatissimus. This fish, while at risk of jumping, actually makes a good adition to a reef, and can keep pest snails and flatworms at bay. I'd recommend one of those, if that's what you're looking for. Here's some more info on that fish (with a couple pictures, bottom of the page).
http://wetwebmedia.com/halichoeresbestart.htm
