Xmas cactus don't have leaves. Each 'branch' is a stem composed of numerous little segments or joints. At the end of each segment are the cells that will initiate new root growth. And more stems, down the road. Stem cuttings won't work unless they are nice and healthy. Don't even bother if the stem sections you're trying to propagate are still soft and wrinkled. Each cutting should consist of three or four segments. Don't be tempted to take large cuttings (with a bunch of segments), as that will greatly reduce your success. I actually never let mine dry out for a few days, but I know that others urge that you do so. As long as you use plenty of perlite in your potting medium, rot will not be a problem. Take as many cuttings as you like. I will typically take three from the same plant and insert them (together) in a small clay pot for rooting and growing. These cuttings result in a well-balanced finished plant. Also, I'd strongly suggest that upon sticking the cuttings into your perlite/potting medium that you drench it then and there. Those cuttings will need moisture in the beginning. Again, by adding plenty of perlite, you reduce the chance of rot. (You can even use 100% perlite, which is what I do.) Attached is an image of a cactus stems consisting of about three segments each.

PG, I'm so glad you said that. I do not grow any of my epiphytic cacti in any peat at all (I have over 200 epiphytes). It's the peat which is more than likely causing your problem. Underwatering is a big problem for CC, people think they need the same care as most other cacti, but they don't they need to be treated like orchids or hoyas. With the peat soil CC come in, even when you do water the water usually runs down the side of the pot and not into the mix. Give it a good soak in warm water then remove as much of the peat as you can, then pot in a well drianing mix. I use 1 part commercial potting mix (peat free) 1 part turface MVP, hydroton, Schultz aquatic soil, or whatever I can find at the moment and 2 parts perlite. My plants have to be watered more often, but they are more healthy and less likely to get fungus and viral infections.

I have an accidental mixture of oxalis and Christmas cactus, but now I love it! I'm very fond of oxalis because it is so easy and stays nice and green in winter and blooms tiny pretty white blooms all the time. I think I might put more things in there, make a bigger mixture, more varied textures. And yes, there are downsides to everywhere we live and grow, but I do love Ohio! I used to go to Florida at least once a year, usually around Christmas (Christmas break from school) and my family would stay with my Gpa, who lived smack dab in the middle of the state, and my parents would do day trips with us to the coasts - we'd drive for hours, spend the day at the beach . . . sigh. :-) I have also been to Sanibel, love that place! And Destin, love it there, too. I'd watch the little hermit crabs and tiny white crabs scurry around. I think the OP was about the cactus and moisture, and I don't have problems with keeping my Christmas cactus moist in winter in Ohio, where it gets really dry inside. I even have one pot of cuttings in a hanging basket, and it's fine moisture-wise, and so pretty - like a firecracker. I have problems with other things, though. I have a dollar store plastic serving tray I got on clearance and I lined it with pea gravel, I keep it moist, it makes a difference. I don't mist the Christmas cactus, I also don't keep it continually moist, I let it dry out, as it is an epiphyte. I think my hanging basket one is the happiest, really, but my mamma plant is just massive, so she's in a big pot on the counter, other plants grouped around her.

Zach, I just saw you posted while I was replying to Liz and Mama! For me to even try to get useable pics I almost always have to move the plants to somewhere other than where they live. Because all of mine hang down below the bottom of the pot I just invert a bowl or “storage container” or something else “neutral” to sit them on while I take the pics, and then they get delivered back home! I also often try to take pics when the sun isn’t shinning (or close the drapes) which helps at least a little bit with “the white problem!” And, in my experience, flash is the worst thing you can do when trying to get a pic that actually looks like the color they are. They really are hard to get accurate pictures of them! But—if you have a BLACK one—I’d be interested!!! ;-) Since it’s so hard to tell from the pics exactly what the colors are, when yours gets big enough, I’d like to get a couple segments of your “salmon” one to—eventually—see how close or different they are. Whenever it works out! And if you have a lot of soil “without roots in it” in that planter, be sure you read all the “stuff” I just posted for Liz about Too Much Water. Until you can get them in smaller pots, be sure you’re letting them dry all the way, and stay dry for a while. Losing them is SAD! I learned that the hard way! Skybird