Don't take branches from trees and put them straight into the cage. They're covered in fungus and diseases, bugs and pests. There's a whole process before they're safe for the cage. This is what I do, some people do it differently.
1. Pick branches with a good diameter and length, from a SAFE tree. The bird's feet should fit about two thirds around the perch.
2. Soak the branches, completely submerged in diluted bleach. For every gallon or two of water, a TBSP bleach. The bleach is dangerous for the birds, so you will have do steps 4 and 5 really well. Another option is white vinegar, it's safer and works ok. If you use the vinegar, you don't need any water. Do this for at least 24 hours.
3. Rinse the branches well and let them soak in fresh, clean water (without the bleach) for a few hours, rinse again and dry.
4. Baking. Set the oven to 200 and bake the branches for about an hour.
5. Set them out in direct sunlight for at least three days, taking them back in when it rains so they don't get wet. The sunlight kills any bleach and fungus left over.
It's not hard, just a lot of waiting.