Chlorhexidine (diluted) is fine to use for "deep cleaning" too. It's all I use- bleach is over-kill & very harsh so every bit must be rinsed away or it's toxic. I do use vinegar on water bowls, but that's not a better disinfectant, it's milder, but it also dissolves hard water deposits, & obviously it must be completely rinsed also. I generally wipe dry the cage & hides when I use chlorhexidine (after they sit about 15-20 minutes for maximum effectiveness) but for wood items (branches or tree-bark tunnels) that are porous, you can just let them dry completely after spraying them. IF you used bleach on those porous (wood) items, they'd be ruined (not safe to use) because the fumes would remain & make your pets sick.