A new experimental procedure combining usual isothermal DC charging and discharging with non-isothermal current measurements has been recently proposed. It is mainly suitable for very high insulating polymers and it was successfully applied to the study of space charge trapping and transport in low-density polyethylene. The analysis of the isothermal currents revealed the presence of different traps whose characteristic (de)trapping times can be deduced. The isothermal procedures allowed the selective charging of the sample. By choosing the charging field and the ratio of charge/discharge times, non-isothermal analysis permitted the differentiation of three or four peaks (at ≈50 C, ≈65 C, ≈70 C and ≈85 C) associated with charge detrapping from surface or near-surface (<20 µm) traps. These traps have activation energies between 0.21 and 1.54 eV. The mobility at 30 C is around 5×10^-16 m² V^-1 s^-1. Samples had to be conditioned before each experiment in order to obtain reproducible results.