  We present an optimal strategy for the relative weighting of different data
modes in inverse problems, and derive the maximum compatibility estimate (MCE)
that corresponds to the maximum likelihood or maximum a posteriori estimates in
the case of a single data mode. MCE is not explicitly dependent on the noise
levels, scale factors or numbers of data points of the complementary data
modes, and can be determined without the mode weight parameters. As a case
study, we consider the problem of reconstructing the shape of a body in $\R^3$
from the boundary curves (profiles) and volumes (brightness values) of its
generalized projections.
