A novel molecular-ink deposition route based on thiourea and N,N-dimethylformamide (DMF) that results in a certified solar cell efficiency world record for non-vacuum deposited CuIn(S,Se)(2) (CIS) absorbers and non-vacuum deposited absorbers with a bandgap of 1.0 eV, is presented. It is found that by substituting the widely employed solvent dimethyl sulfoxide with DMF, the coordination chemistry of InCl3 could be altered, dramatically improving ink stability, enabling up to tenfold increased concentrations, omitting the necessity for elevated ink temperatures, and radically accelerating the deposition process. Furthermore, it is shown that by introducing compositionally graded precursor films, film porosity, compositional gradients, and the surface roughness of the absorbers are effectively reduced and device conversion efficiencies are increased up to 13.8% (13.1% certified, active area). The reduced roughness is also seen as crucial to realize monolithically interconnected CIS-perovskite tandem devices, where semitransparent MAPbI(3) devices are directly deposited on the CIS bottom cell. Confirming the feasibility of this approach, monolithic devices with near perfect voltage addition between subcells of up to 1.40 V are presented.