  We perform a comprehensive study of the allowed parameter space of the Two
Higgs Doublet Model of Type II (2HDM-II). Using the theoretical framework
flavio we combine the most recent flavour, collider and electroweak precision
observables with theoretical constraints to obtain bounds on the mass spectrum
of the theory. In particular we find that the 2HDM-II fits the data slightly
better than the Standard Model (SM) with best fit values of the heavy Higgs
masses around 2 TeV and a value of $\tan \beta \approx 4$. Moreover, we
conclude that the wrong-sign limit is disfavoured by Higgs signal strengths and
excluded by the global fit by more than five standard deviations and potential
deviations from the alignment limit can only be tiny. Finally we test the
consequences of our study on electroweak baryogenesis via the program package
BSMPT and we find that the allowed parameter space strongly discourages a
strong first order phase transition within the 2HDM-II.
