We discuss the value of the cosmological constant as recovered from cosmic microwave background (CMB) and large scale structure (LSS) data and the robustness of the results when general isocurvature initial conditions are allowed for, as opposed to purely adiabatic perturbations. The Bayesian and frequentist statistical approaches are compared. It is shown that pre-WMAP CMB and LSS data tend to be incompatible with a non-zero cosmological constant, regardless of the type of initial conditions and of the statistical approach. The non-adiabatic contribution is constrained to be ⩽40% (2σ c.l.).