Let
T
i
,
i
=
1
,
2
{T_i},i = 1,2
, be measurable transformations which define bounded composition operators
C
T
i
{C_{{T_i}}}
on
L
2
{L^2}
of a
σ
\sigma
-finite measure space. Denote their respective Radon-Nikodym derivatives by
h
i
,
i
=
1
,
2
{h_i},i = 1,2
. The main result of this paper is that if
h
i
∘
T
i
≤
h
j
,
i
,
j
=
1
,
2
{h_i} \circ {T_i} \leq {h_j},i,j = 1,2
, then for each of the positive integers
m
,
n
,
p
m,n,p
the operator
[
C
T
1
m
C
T
2
n
]
p
{[C_{{T_1}}^mC_{{T_2}}^n]^p}
is hyponormal. As a consequence, we see that the sufficient condition established by Harrington and Whitley for hyponormality of a composition operator is actually sufficient for all powers to be hyponormal.