  Let B be a block of a finite group with respect to an algebraically closed
field F of characteristic p>0. In a recent paper, Otokita gave an upper bound
for the Loewy length LL(ZB) of the center ZB of B in terms of a defect group D
of B. We refine his methods in order to prove the optimal bound LL(ZB)\le
LL(FD) whenever D is abelian. We also improve Otokita's bound for non-abelian
defect groups. As an application we classify the blocks B such that LL(ZB)\ge
|D|/2.
