Does the single piece serve a utility? Meaning, generally, does it serve a tangible purpose? A thumbtack, for example, serves such a purpose (it helps secure something in place), as does a toilet plunger (it helps un-clog a toilet). That's really all that matters. That, and it's gotta be novel, and non-obvious...but just because something is a single piece does not mean it will be considered obvious.
There you have a short answer, but its really that simple. Its a somewhat vague answer, but anything less vague might not be accurate.
And for what it's worth, even if the single piece is not novel, say it's an ordinary stick, you can still patent a novel and non-obvious method of using that stick.
