[en] We extend our investigation of backgrounds to new physics signals, following CMS’s data-driven search for supersymmetry at the LHC. The aim is to use different sets of cuts in γ+3-jet production to predict the irreducible Z+3-jet background (with the Z boson decaying to neutrinos) to searches with E̸T+3-jet signal topologies. We compute ratios of Z+3-jet to γ+3-jet production cross sections and kinematic distributions at next-to-leading order (NLO) in αs. We compare these ratios with those obtained using a parton shower matched to leading-order matrix elements (ME+PS). This study extends our previous work [Bern et al., Phys. Rev. D 84 114002 (2011)] on the Z+2-jet to γ+2-jet ratio. We find excellent agreement with the ratio determined from the earlier NLO results involving two instead of three jets, and agreement to within 10% between the NLO and ME+PS results for the ratios. We also examine the possibility of large QCD logarithms in these processes. Ratios of Z+n-jet to γ+n-jet cross sections are plausibly less sensitive to such corrections than the cross sections themselves. Their effect on estimates of Z+3-jet to γ+3-jet ratios can be assessed experimentally by measuring the γ+3-jet to γ+2-jet production ratio in search regions. We partially address the question of potentially large electroweak logarithms by computing the real-emission part of the electroweak corrections to the ratio using ME+PS and find that it is 1% or less. Our estimate of the remaining theoretical uncertainties in the Z to γ ratio is in agreement with our earlier study.