The short-range parimagnetic configurations, observed in the heavy rare-earth RCo2 compounds in paramagnetic range far above the Curie temperature TC, consist in formation of ferromagnetic cobalt clusters antiferromagnetically coupled to the neighboring R magnetic moments. The characteristic temperature of the onset of parimagnetism Tf is very sensitive to changes of external conditions like pressure or composition. The pressure coefficients δTf/ δp and δTC/ δp are comparable, indicating a close connection of underlying mechanisms. Our recent measurements indicate systematic evolution of the pressure coefficients with spanning the rare-earth series from Dy through Tm in RCo2 with a specific case TmCo2.