  We describe a method to measure and subtract the incoherent component of
energy flow arising from multiple interactions from jet shape/substructure
observables of ultra-massive jets. The amount subtracted is a function of the
jet shape variable of interest and not a universal property. Such a correction
is expected to significantly reduce any bias in the corresponding distributions
generated by the presence of multiple interactions, and to improve measurement
resolution. Since in our method the correction is obtained from the data, it is
not subject to uncertainties coming from the use of theoretical calculations
and/or Monte Carlo event generators. We derive our correction method for the
jet mass, angularity and planar flow. We find these corrections to be in good
agreement with data on massive jets observed by the CDF collaboration. Finally,
we comment on the linkage with the concept of jet area and jet mass area.
