Seven existing relationships between monthly mean clearness index and the number of bright sunshine hours are tested under the climate and latitude of Romania. New (best-fit) correlations are derived. They use bright sunshine hour number or fractional total cloud amount as input. The dependence of the new sunshine-based regressions on month is stronger than their dependence on latitude. They generally underestimate the clearness index in the first half-year and overestimate it in the rest of the year. The accuracy of the new regression seems not to depend significantly on the year.