  Using Robert Spira's \cite{D} definitions of complex Mersenne numbers and the
complex sum-of-divisors function, we characterize $(\omega+2)$-norm-perfect and
$(\omega+2)$-perfect numbers that are divisble by $\omega+2$ and prove the
nonexistence of $2$-norm-perfect numbers that are divisible by $2$ in the
Eisenstein integers.
