We investigate the use of extracellular action potential (EAP) recordings for biophysically faithful compartmental models. We ask whether constraining a model to fit the EAP is superior to matching the intracellular action potential (IAP). In agreement with previous studies, we find that the IAP method under-constrains the parameters. As a result, significantly different sets of parameters can have virtually identical IAP's. In contrast, the EAP method results in a much tighter constraint. We find that the distinguishing characteristics of the waveform--but not its amplitude-resulting from the distribution of active conductances are fairly invariant to changes of electrode position and detailed cellular morphology. Based on these results, we conclude that EAP recordings are an excellent source of data for the purpose of constraining compartmental models.