  We prove the Alperin-McKay Conjecture for all $p$-blocks of finite groups
with metacyclic, minimal non-abelian defect groups. These are precisely the
metacyclic groups whose derived subgroup have order $p$. In the special case
$p=3$, we also verify Alperin's Weight Conjecture for these defect groups.
Moreover, in case $p=5$ we do the same for the non-abelian defect groups
$C_{25}\rtimes C_{5^n}$. The proofs do not rely on the classification of the
finite simple groups.
