In bird/wildlife photography good composition in a shot often means much more than just positioning an eye or subject in the proper part of the frame based on a grid of thirds or a point on the golden spiral.
The following are my thoughts and considerations and shouldn't be taken as gospel. In every case there can be exceptions to rules.
It is usually a better image if there is "room" for the subject to move or look into, particularly if the subject is in motion.
Eye contact with the subject for the viewer usually makes for a better shot unless what the subject is interested in is also in the image.
Proctocology shots are usually rubbish bin candiates, what is a procto shot? Any image where the ass presents itself to the viewer first. Shooting high to a perched subject or only catching a flight shot on the outbound leg are very common examples. Images where the bird is perched away and turned back to the camera are an exception if the eye is in focus and not the tail feathers.
Point of view is big contributor to a nicely composed image, like mentioned before shooting up to a subject is rarely a good thing, the same is shooting down to the same. Shooting at eye level usually brings a greater impact into the image.
This can be more of a personal issue but I feel that using the depth of field to capture the subject sharp and crisp whether just eyes or the whole subject but leaving the areas of in focus at that point and having everything else fall out of focus makes for a better image.
And one of toughest issues to control is the surrounds of the subject, in particular the fore and background. Too "busy" with branches, weeds, vines and all the other that is the subjects home can bring an image down. Having a clean surrounds brings more attention to the subject. Even minor issues will detract an image more than might be expected. And shooting warblers isn't making this any easier because of where they are found.
In your image below if I had shot it there are a couple things I might try to work.
First the oof branch/blade in the upper right poking into the frame. Adds nothing to the image, and as the brightest part of that part of the frame draws the eye away from the subject. Needs to go away.
The large branch nearest to the subject seems to restrain the subject inside a border, one could try to remove, modify or ignore it. Not an easy choice but in this case I would leave it alone because of something more important IMO.
And that is the eye contact or lack of, the subject is looking back and up. It isn't making contact with the viewer and "we" aren't sharing it's view of whatever it might be scanning. If the head was tilted down the viewer would have more of a contact with the little guy.
Because of this view we have I wouldn't spend a lot of time in post on this shot. It isn't the perfect look I want from a subject so it isn't worth the time for ME to work it.
Your image is well exposed and looks to have been in reasonable focus, however the lack of fine detail denotes to me either a rather large crop or maybe a noise reduction pass that washed the finer details away. Either way the subject is in that range where one might want to pull in closer but the detail isn't there or pull back from the subject and have more of a enviormental image. For me I would pull back, I want to resolve the fine details and having a "washed smooth" portion of the subject doesn't work for me.
The following are not images I consider first rate, they all are some that I maybe should have deleted because all of the elements that make a great shot, I just missed the mark on one or two points.
Clean Background and tight dof
No eye contact but sharing the view
Busy backgrounds but add to mood or complement subject colors