Elmendorf, Kriz, Mandell and May have used their technology of modules over highly structured ring spectra to give new constructions of
M
U
MU
-modules such as
B
P
BP
,
K
(
n
)
K(n)
and so on, which makes it much easier to analyse product structures on these spectra. Unfortunately, their construction only works in its simplest form for modules over
M
U
[
1
2
]
∗
MU[\frac {1}{2}]_*
that are concentrated in degrees divisible by
4
4
; this guarantees that various obstruction groups are trivial. We extend these results to the cases where
2
=
0
2=0
or the homotopy groups are allowed to be nonzero in all even degrees; in this context the obstruction groups are nontrivial. We shall show that there are never any obstructions to associativity, and that the obstructions to commutativity are given by a certain power operation; this was inspired by parallel results of Mironov in Baas-Sullivan theory. We use formal group theory to derive various formulae for this power operation, and deduce a number of results about realising
2
2
-local
M
U
∗
MU_*
-modules as
M
U
MU
-modules.