In atmospheric fatigue, intrinsic threshold stress intensity, K_th, far from being a material constant, varies significantly. It is controlled by a certain computable, load-history sensitive, near-tip residual stress, s*, that appears to moderate crack-tip diffusion kinetics and thereby determines K_th, the incremental K required for an open crack to extend by fatigue. This demands reconsideration of the relationship between near-threshold crack growth rates and applied effective stress intensity range, DK_eff. Its practical implementation requires considerations of Linear Hysteretic Fracture Mechanics (LHFM). LHFM is applied to translate applied K, to near-tip cyclic inelastic stress-strain response. A procedure is described to separate intrinsic threshold stress intensity from ‘extrinsic’ component for a known DK_th, obtained by conventional means. This opens the way to engineering application of the vast amount of available legacy fatigue threshold data obtained on long cracks by load shedding techniques. The new relationships permit extension of fracture mechanics considerations to short cracks including defects in additive manufactured materials and naturally forming cracks in components over high-cycle and very high-cycle (HCF/VHCF) regimes. Most importantly, the new approach permits handling near-threshold fatigue response both under constant amplitude as well as under variable-amplitude loading, representative of actual service conditions. It also permits re-interpretation of test data obtained by the so-called cyclic R-curve and compression-compression pre-cracking techniques.