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Let 
$ZB$ be the center of a 
$p$-block 
$B$ of a finite group with defect group 
$D$. We show that the Loewy length 
$LL(ZB)$ of 
$ZB$ is bounded by 
$|D|/p+p-1$ provided 
$D$ is not cyclic. If 
$D$ is nonabelian, we prove the stronger bound 
$LL(ZB)<\min \{p^{d-1},4p^{d-2}\}$ where 
$|D|=p^{d}$. Conversely, we classify the blocks 
$B$ with 
$LL(ZB)\geqslant \min \{p^{d-1},4p^{d-2}\}$. This extends some results previously obtained by the present authors. Moreover, we characterize blocks with uniserial center.
