A new computational technique has been developed to simulate charge transport in dilute, energetically random, media. The results predict that in materials containing 15-20% hopping sites, the transition from field-assisted to field-saturated drift occurs within a field range of 10 5 -10 6 V/cm, lower values referring to lower degrees of energetic disorder. Experimental results are reported for N,N -diphenyl-N,N -bis(3-methylphenyl)-[1,1 -biphenyl]-4,4 -diamine (TPD) and 5 -[4-[bis(4-ethylphenyl)amino]-phenyl]-N,N,N ,N -tetrakis(4-ethylphenyl) [1,1 :3 ,1 -terphenyl]-4,4 -diamine (EFTP) doped in either a polycarbonate (PC) or poly (styrene) (PS). While TPD doped PS fulfills all criteria of disorder controlled hopping, a superposition of disorder and polaron effects has to be invoked for EFTP in both PC or PS, the latter resulting from coupling of the charge transfer process to a torsional mode of the dopant molecule. Criteria to separate disorder and polaron effects in experimental data are briefly outlined.