  Kinematic selection cuts and isolation requirements are a necessity in
experimental measurements for identifying prompt leptons and photons that
originate from the hard-interaction process of interest. We analyze how such
cuts affect the application of the $q_T$ and $N$-jettiness subtraction methods
for fixed-order calculations. We consider both fixed-cone and smooth-cone
isolation methods. We find that kinematic selection and isolation cuts both
induce parametrically enhanced power corrections with considerably slower
convergence compared to the standard power corrections that are already present
in inclusive cross sections without additional cuts. Using analytic arguments
at next-to-leading order we derive their general scaling behavior as a function
of the subtraction cutoff. We also study their numerical impact for the case of
gluon-fusion Higgs production in the $H\to\gamma\gamma$ decay mode and for
$pp\to\gamma\gamma$ direct diphoton production. We find that the relative
enhancement of the additional cut-induced power corrections tends to be more
severe for $q_T$, where it can reach an order of magnitude or more, depending
on the choice of parameters and subtraction cutoffs. We discuss how all such
cuts can be incorporated without causing additional power corrections by
implementing the subtractions differentially rather than through a global
slicing method. We also highlight the close relation of this formulation of the
subtractions to the projection-to-Born method.
