Constraining the composition of super-Earth-to-sub-Neptune-size planets is a priority to understand the processes of planetary formation and evolution . \pi Men c represents a unique target for the atmospheric and compositional characterization of such planets because it is strongly irradiated and its bulk density is consistent with abundant H _ { 2 } O . We searched for hydrogen from photodissociating H _ { 2 } /H _ { 2 } O in \pi Men c ’ s upper atmosphere through H i Ly \alpha transmission spectroscopy with the Hubble Space Telescope ’ s STIS instrument , but did not detect it . We set 1 \sigma ( 3 \sigma ) upper limits for the effective planet-to-star size ratio R _ { Ly \alpha } / R _ { \star } =0.13 ( 0.24 ) and 0.12 ( 0.20 ) at velocities [ - 215 , - 91 ] km/s and [ + 57 , + 180 ] km/s , respectively . We reconstructed the stellar spectrum , and estimate that \pi Men c receives about 1350 erg cm ^ { -2 } s ^ { -1 } of 5–912-Å-energy , enough to cause rapid atmospheric escape . An interesting scenario to explain the non-detection is that \pi Men c ’ s atmosphere is dominated by H _ { 2 } O or other heavy molecules rather than H _ { 2 } /He . According to our models , abundant oxygen results in less extended atmospheres , which transition from neutral to ionized hydrogen closer to the planet . We compare our non-detection to other detection attempts , and tentatively identify two behaviors : planets with densities \lesssim 2 g cm ^ { -3 } ( and likely hydrogen-dominated atmospheres ) result in H i Ly \alpha absorption , whereas planets with densities \gtrsim 3 g cm ^ { -3 } ( and plausibly non-hydrogen-dominated atmospheres ) do not result in measurable absorption . Investigating a sample of strongly-irradiated sub-Neptunes may provide some statistical confirmation if it is shown that they do not generally develop extended atmospheres .