What software do you use for your photos? I find that LR4 will easily clean that type of noise with about 1/4 of the NR slider. Then using the sharpening masking you can narrow the sharpening to just the bird and perch. These are the two reasons I've made the switch from Aperture to LR. Aperture has horrible NR tools and only so-so sharpening but no sharpening masking. Otherwise great shot.
I took the liberty to do as I described with your jpeg. RAW would be better.