We consider
p
p
-blocks with abelian defect groups and in the first part prove a relationship between its Loewy length and that for blocks of normal subgroups of index
p
p
. Using this, we show that if
B
B
is a
2
2
-block of a finite group with abelian defect group
D
≅
C
2
a
1
×
⋯
×
C
2
a
r
×
(
C
2
)
s
D \cong C_{2^{a_1}} \times \cdots \times C_{2^{a_r}} \times (C_2)^s
, where
a
i
>
1
a_i > 1
for all
i
i
and
r
≥
0
r \geq 0
, then
d
>
LL
(
B
)
≤
2
a
1
+
⋯
+
2
a
r
+
2
s
−
r
+
1
d > \operatorname {LL}(B) \leq 2^{a_1}+\cdots +2^{a_r}+2s-r+1
, where
|
D
|
=
2
d
|D|=2^d
. When
s
=
1
s=1
the upper bound can be improved to
2
a
1
+
⋯
+
2
a
r
+
2
−
r
2^{a_1}+\cdots +2^{a_r}+2-r
. Together these give sharp upper bounds for every isomorphism type of
D
D
. A consequence is that when
D
D
is an abelian
2
2
-group the Loewy length is bounded above by
|
D
|
|D|
except when
D
D
is a Klein-four group and
B
B
is Morita equivalent to the principal block of
A
5
A_5
. We conjecture similar bounds for arbitrary primes and give evidence that it holds for principal
3
3
-blocks.