A detailed comparison of HERA data at low Bjorken-x and low four-momentum-transfer squared, Q2, with predictions based on lnQ2 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, FL. This additional term, FLALHT/Q2, improves the description of the reduced cross sections significantly. The resulting predictions for FL suggest that further corrections are required for Q2 less than about 2 GeV2.