  Let p\in\{2,3\}, and let k be an imaginary quadratic field in which p
decomposes into two distinct primes \mathfrak{p} and \bar{\mathfrak{p}}. Let
k_\infty be the unique Z_p-extension of k which is unramified outside of
\mathfrak{p}, and let K_\infty be a finite extension of k_\infty, abelian over
k. We prove that in K_\infty, the projective limit of the p-class group and the
projective limit of units modulo elliptic units share the same \mu-invariant
and the same \lambda-invariant. Then we prove that up to a constant, the
characteristic ideal of the projective limit of the p-class group coincides
with the characteristic ideal of the projective limit of units modulo elliptic
units.
