Multiple high-precision β-decay measurements are being carried out these days on various nuclei, in search of Beyond the Standard Model signatures. Those necessitate very accurate Standard Model theoretical forecasts to be compared with. Motivated by the experimental surge, I will present a general formalism for a precise calculation of β-decay observables, with controlled accuracy, based on a perturbative analysis of the theoretical observables related to the phenomena, including, e.g., high-order nuclear recoil and shape corrections. The accuracy of the corrections will be analyzed by identifying a hierarchy of small parameters, related to the low momentum transfer characterizing β-decays. Concentrating on nuclei relevant to the ongoing experiments, I will examine highly accurate standard model numerical forecasts of the β-neutrino correlation coefficients and β-energy spectrum for 6He and 23Ne, compare them to existing as well as new measurements and show new significant constraints on the Standard Model.