  Motivated by the large difference between the direct CP asymmetries
$A_{CP}(B^-\to \pi^0 K^-)$ and $A_{CP}(\bar{B}^{0}\to \pi^{+} K^{-})$, we
combine the up-to-date experimental information on $B\to\pi K$, $\pi K^{\ast}$
and $\rho K$ decays to pursue possible solutions with the nonuniversal
$Z^{\prime}$ model. Detailed analyses of the relative impacts of different
types of couplings are presented in four specific cases. Numerically, we find
that the new coupling parameters, $\xi^{LL}$ and $\xi^{LR}$ with a common
nontrivial new weak phase $\phi_L\sim-86^{\circ}$, which are relevant to the
$Z^{\prime}$ contributions to the electroweak penguin sector $\triangle C_9$
and $\triangle C_7$, are crucial to the observed "$\pi K$ puzzle". Furthermore,
they are found to be definitely unequal and opposite in sign. We also find that
$A_{CP}(B^-\to \rho^0 K^-)$ can put a strong constraint on the new $Z^{\prime}$
couplings, which implies the $Z^{\prime}$ contributions to the coefficient of
QCD penguins operator $O_3$ involving the parameter $\zeta^{LL}$ required.
