<p>Several of the icy satellites in the outer Solar System have or had an ocean underneath their ice-covered surfaces. As the ice shell changes thickness, the volume change that accompanies the phase transition between liquid water and solid ice creates stresses in the ice shell and changes the pressure in the underlying ocean. A thinning ice shell develops compressive stresses within the cold, elastic ice near the surface, and the pressure in the ocean decreases. Here we show that ice-shell thinning can lead to two possible outcomes, depending on the size of the icy body. For the smallest icy bodies, such as Mimas, Enceladus and Miranda, the pressure may become low enough that water reaches the boiling temperature, generating buoyant water vapour and exsolved gases. Boiling conditions are reached while the compressive stresses are lower than the compressive strength of ice, which explains why an emerging (growing) ocean is compatible with a lack of compressive tectonic features on these worlds. For bodies larger than ~300 km radius, such as Titania and Iapetus, thinning of the ice shell by ~10% would lead to compressive failure, thus providing a driving mechanism for compressional tectonic features. Although the signature of ancient ocean development may be overprinted by later cratering, a lack of compressional features on larger worlds may rule out recent oceans.</p>