The Standard Penetration Test has become increasingly popular in testing stiff to hard cohesive soils. Several correlations have been proposed that associate undrained shear strength with SPT blowcount in such soils. These correlations, often produced through significant data scatter, are typically restricted to specific materials and their main drawback is their not taking into account physical characteristics, often conveniently reflected in trivial lab processes, e.g. clay mineralogy manifested through Atterberg limits. A simplified empirical relationship is presented that correlates the undrained shear strength (c_u) of cohesive formations and the ‘as-measured’ SPT blowcount (N) attempting to reduce statistical scatter by addressing the important influence of characteristic physical properties on soil strength. The correlation derives from the statistical processing of data obtained in three different stiff to very hard cohesive formations in Greece, essentially clays and marls, each exhibiting a consistently identifiable geotechnical behaviour, in which a large number of ‘coupled’ SPT and lab UU triaxial tests were performed. Processing of the available data supports the common observation that the definition of a constant c_u / N ratio (even within the same material) is unrealistic. The inclusion of both water content (w) and plasticity index (PI) in such correlations is investigated and found to significantly improve the consistency of correlation results, indicating a linear dependence of the c_u / N ratio on (w) and logarithmic dependence on (PI). The identification of additional independent parameters affecting the procedure is also examined and basic directions for the orientation of future correlations are outlined.