The resummed Drell-Yan cross section in the double-logarithmic approximation suffers from infrared renormalons. Their presence was interpreted as an indication for nonperturbative corrections of order #LAMBDA#_Q_C_D/(Q(1-z)). We find that, once soft gluon emission is accurately taken into account, the leading renormalon divergence is cancelled by higher-order perturbative contributions in the exponent of the resummed cross section. From this evidence, ''higher twist'' corrections to the hard cross section in Drell-Yan production should intervene only at order #LAMBDA#"2_Q_C_D/(Q"2(1-z)"2) in the entire perturbative domain Q(1-z)>#LAMBDA#_Q_C_D. We compare this result with hadronic event shape variables, comment on the pote...