  We study constraints on time variation of the fine structure constant alpha
from cosmic microwave background (CMB) taking into account simultaneous change
in alpha and the electron mass m_e which might be implied in unification
theories. We obtain the constraints -0.097 < Delta alpha/alpha < 0.034 at 95%
C.L. using WMAP data only, and -0.042 < Delta alpha/alpha < 0.026 combining
with the constraint on the Hubble parameter by the HST Hubble Key Project.
These are improved by 15% compared with constraints assuming only alpha varies.
We discuss other relations between variations in alpha and m_e but we do not
find evidence for varying alpha.
