  Constraining the planetary composition is essential for exoplanetary
characterization. In this paper, we use a statistical analysis to determine the
characteristic maximum (threshold) radii for various compositions for
exoplanets with masses up to 25 Earth masses (M$_\oplus$). We confirm that most
planets with radii larger than 1.6 Earth radius (R$_\oplus$) are not rocky, and
must consist of lighter elements, as found by previous studies. We find that
planets with radii above 2.6 R$_\oplus$ cannot be pure-water worlds, and must
contain significant amounts of hydrogen and helium (H-He). We find that planets
with radii larger than about 3 R$_\oplus$, 3.6 R$_\oplus$, and 4.3 R$_\oplus$
are expected to consist of 2%, 5% and 10% of H-He, respectively. We investigate
the sensitivity of the results to the assumed internal structure, the planetary
temperature and albedo, and the accuracy of the mass and radius determination.
We show that the envelope's metallicity, the percentage of H-He and the
distribution of the elements play a significant role in the determination of
the threshold radius. Finally, we conclude that despite the degenerate nature
of the problem, it is possible to put limits on the possible range of
compositions for planets with well-measured mass and radius.
