We generalize the Knill-Laflamme condition to the problem of using a given noisy channel N to approximately simulate another given channel M. In particular, this yields a way to compute a near-optimal error for approximate subsystem quantum error correction. For approximate QEC, this also yield a near-optimal recovery channel. We use this result to derive a simple necessary and sufficient condition for lowest order perturbative QEC. That is, given a noise model function of a small parameter, to determine whether a given code can correct it up to lowest order in the fidelity.