The pair-crossing number of a graph G, pcrG, is the minimum possible number of pairs of edges that cross each other possibly several times in a drawing of G. It is known that there is a constant ci¾?1/64 such that for every not too sparse graph G with n vertices and m edges ${\mbox{pcr}}G \geq c \frac{m^3}{n^2}$ . This bound is tight, up to the constant c. Here we show that ci¾?1/34.2 if G is drawn without adjacent crossings.