A detailed comparison of HERA data at low Bjorken-x and low four-momentum-transfer squared, Q(2), with predictions based on lnQ(2) evolution (DGLAP) in perturbative quantum chromodynamics suggests inadequacies of this framework. The standard DGLAP evolution was augmented by including an additional higher-twist term in the description of the longitudinal structure function, F-L. This additional term, F(L)A(L)(HT) / Q(2), improves the description of the reduced cross sections significantly. The resulting predictions for FL suggest that further corrections are required for Q(2) less than about 2 GeV2.