We present a Bayesian re-analysis of the sky-averaged 21-cm experimental data from SARAS2 using nested sampling implemented with , spectrally smooth foreground modelling implemented with , detailed systematic modelling and rapid signal emulation with . Our analysis differs from previous analysis of the SARAS2 data through the use of a full Bayesian framework and separate modelling of the foreground and non-smooth systematics present in the data. We use the most up-to-date global signal models including Lyman-𝛼 and CMB heating and parameterised by astrophysical parameters such as star formation efficiency, X-ray heating efficiency, minimal virial circular velocity, CMB optical depth and the low energy cutoff of the X-ray spectral energy distribution. We also consider models with an excess radio background above the CMB produced via radio emission from early galaxies and parameterised by a radio production efficiency. A non-smooth systematic is identified and modelled as both a frequency damped sinusoid introduced by the electronics and separately from the sky. The latter is modulated by the total efficiency of the antenna and marginally favoured by the data. We consider three models for the noise in the data with different frequency dependencies. We find that the SARAS2 constraints on individual astrophysical parameters are extremely weak however we identify classes of disfavoured signals. Specifically, we weakly disfavour standard astrophysical models with high Lyman-𝛼 fluxes and generally weak heating and more confidently disfavour exotic models with high Lyman-𝛼 fluxes, low X-ray efficiencies, high radio production efficiencies in early galaxies and high CMB optical depths. We intend to follow this work up with a similar analysis of the recently published SARAS3 data.