  Gy\'arf\'as conjectured in 2011 that every $r$-edge-colored $K_n$ contains a
monochromatic component of bounded ("perhaps three") diameter on at least
$n/(r-1)$ vertices.
  Letzter proved this conjecture with diameter four.
  In this note we improve the result in the case of $r=3$: We show that in
every $3$-edge-coloring of $K_n$ either there is a monochromatic component of
diameter at most three on at least $n/2$ vertices or every color class is
spanning and has diameter at most four.
