Efforts to improve organic field-effect transistors (OFETs) have so far concentrated mainly on their field-effect mobility, but another important parameter is the on-off ratio, i.e., the ratio of the saturation current at maximum absolute gate voltage (V-g) to that at zero V-g. It is shown how an understanding of the so-called ''ohmic'' current, which reduces this ratio, will perhaps lead to improved performances now it has been recognized that this current is connected with mobile dopants.