  Continuing the study of the Iwasawa theory of symmetric powers of CM modular
forms at supersingular primes begun by the first author and Antonio Lei, we
prove a Main Conjecture equating the "admissible" $p$-adic $L$-functions to
characteristic ideals of "finite-slope" Selmer modules constructed by the
second author. As a key ingredient, we improve Rubin's result on the Main
Conjecture of Iwasawa theory for imaginary quadratic fields to an equality at
inert primes.
