  Enceladus's gravity and shape have been explained in terms of a thick
isostatic ice shell floating on a global ocean, in contradiction of the thin
shell implied by librations. Here we propose a new isostatic model minimizing
crustal deviatoric stress, and demonstrate that gravity and shape data predict
a $\rm{38\pm4\,km}$-thick ocean beneath a $\rm{23\pm4\,km}$-thick shell
agreeing with -- but independent of -- libration data. Isostatic and tidal
stresses are comparable in magnitude. South polar crust is only $7\pm4\rm\,km$
thick, facilitating the opening of water conduits and enhancing tidal
dissipation through stress concentration. Enceladus's resonant companion,
Dione, is in a similar state of minimum stress isostasy. Its gravity and shape
can be explained in terms of a $\rm{99\pm23\,km}$-thick isostatic shell
overlying a $\rm{65\pm30\,km}$-thick global ocean, thus providing the first
clear evidence for a present-day ocean within Dione.
