  We present calculations of shell-model effective interactions for both
degenerate and non-degenerate model spaces using the Krenciglowa-Kuo (KK) and
the extended Krenciglowa-Kuo iteration method recently developed by Okamoto,
Suzuki {\it et al.} (EKKO). The starting point is the low-momentum
nucleon-nucleon interaction $V_{low-k}$ obtained from the N$^3$LO chiral
two-nucleon interaction. The model spaces spanned by the $sd$ and $sdpf$ shells
are both considered. With a solvable model, we show that both the KK and EKKO
methods are convenient for deriving the effective interactions for
non-degenerate model spaces. The EKKO method is especially desirable in this
situation since the vertex function $\hat Z$-box employed therein is well
behaved while the corresponding vertex function $\hat Q$-box employed in the
Lee-Suzuki (LS) and KK methods may have singularities. The converged
shell-model effective interactions given by the EKKO and KK methods are
equivalent, although the former method is considerably more efficient. The
degenerate $sd$-shell effective interactions given by the LS method are
practically identical to those from the EKKO and KK methods. Results of the
$sd$ one-shell and $sdpf$ two-shell calculations for $^{18}$O, $^{18}$F,
$^{19}$O and $^{19}$F using the EKKO effective interactions are compared, and
the importance of the shell-model three-nucleon forces is discussed.
