Here is Ver. 1, with just decrease in brightness of perch and lowered perch contrast. No change in bird itself, but to my eye it really pops out now that the perch isn't so bright.
Ver. 2. Cropped out a lot of the perch to reduce its impact. Darkened and decreased the contrast of highlights in background. Sharpened the eye a bit.
Not a finished product, but I hope it shows some options for you. The quality is really starting to suffer from compression and the small size file I was working with.
I wouldn't have cropped as tight except for my desire to minimize the perch.