Small Bird in Southwest Tennessee (Description Only)

I have seen this bird twice recently, and (s)he's gone as soon as (s)he spots me. I have lots of Sparrows and feed them daily, but this bird is smaller than most of them and has a different beak. It is dark in color, longer than a Sparrow's and slender. The bird is medium brown with a light brown underside. As for markings, the only thing I got a good look at was a light brown or tan eyebrow. Both times, (s)he chose a suet cake that was in a basket about 6-7 feet off the ground, unlike the Sparrows, who go for birdseed, etc. in a bowl on the ground. Also, this bird came to feed alone, unlike my regular patrons, who usually travel in numbers.

Can you suggest some birds, based on the above facts, that I might look into in an attempt to identify my mystery guest?

Possibly a Wren.... I would look up Wren's and you may find your bird.

Also look up Brown Creeper.