Time-of-flight measurements on molecularly doped polymers have revealed that, the transient current shapes change from being virtually non-dispersive to highly dispersive (featureless) and back to non-dispersive as the shallow trap concentration is increased from 0 to ∼ 1 mol%. The shallow traps were introduced into the molecularly doped system by mixing the charge-transporting molecule with small amounts of another transporting molecule having a significantly lower ionization potential. The results support the model of Schmidlin for single-trap-controlled transport. Based on this model, the attempt-to-escape frequency and the activation energy for escape from the trap are found to be ∼4 × 1012s−1and 0·56eV, respectively.