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Isolated photon production at hadron colliders proceeds via direct production and fragmentation processes. Theory predictions for the isolated photon and photon-plus-jet cross section often impose idealised photon isolation criteria, eliminating the fragmentation contribution and introducing a systematic uncertainty in the comparison to data. We present NNLO predictions for the photon-plus-jet cross section with the experimental isolation including both, direct and fragmentation contributions. Predictions with two different parton-to-photon fragmentation functions are compared, allowing for an estimation of the uncertainty stemming from the only loosely constrained photon fragmentation functions.