Europa and energy transfer

NASA has a mission to the Jovian system, to study Europa. That moon is interesting because it appears to have liquid water under an icy surface. The heat need to keep the water liquid comes from the stretching and compression Europa experiences during its orbit around Jupiter, the orbit not been exactly circular.
So much, so simple.
Some thought made me realise that although the tidal forces on Europa mean that it is not exactly spherical, its two bulges cannot remain perfectly aligned with Jupiter, because Europa's angular velocity relative to Jupiter is higher at periapsis than at apoapsis. The result is that the nearer bulge is sometimes ahead, and sometimes behind, relative to Europa's orbital motion, resulting in a net force backwards along the orbit, or forward along the orbit.
Again, certainly stuff that's already well known.
As far as I can see, the energy that is being dissipated as heat inside Europa has to come from changes to Europa's orbit. Further, if Europa were either perfectly rigid, or perfectly elastic, there would be no energy transfer, and consequently no change to the orbit.
It would make no difference if Jupiter itself were perfectly rigid, so the transfer cannot involve tides on Jupiter generated by Europa.
So the existence of the orbital energy transfer depends on Europa being neither perfectly rigid nor perfectly elastic.
What escapes me is the mechanism.
Any thoughts?