High dispersion of data, created by time history analyses (THA) for developing fragility curves (FCs), results in remarkable uncertainty in risk evaluation. Regarding the lack of studies on uncertainty reduction of FCs of electric power equipment, this paper presents three means for reducing this dispersion: 1) using spectral acceleration at fundamental period of the system, Sa(T1), instead of peak ground acceleration (PGA) as the intensity measure (IM), 2) using Sa(T1)+Sa(T2), as the IM, and 3) using a set of scenario earthquakes for THA instead of randomly chosen accelerograms. The methods were compared for two key structures of electric substations, a post insulator (PI) and a current transformer (CT). For the PI, first a set of randomly chosen accelerograms was employed, once using PGA, and once more Sa(T1) as the IM, and then a set of scenario-based records, with the same IMs. For the CT, PGA, Sa(T1) and Sa(T1)+Sa(T2) were used as the IM. Results show that using scenario-compatible records leads to more consistent data for developing the FCs, and that this consistency gets better and much better, respectively, by using Sa(T1) and Sa(T1)+Sa(T2) as the IM. It is suggested that for very high frequency systems, such as PI, Sa(T1) is used, while for moderate- and low-frequency systems, such as CT, Sa(T1)+Sa(T2) is used.