A multi-peaked version of the analytically extendedfunction (AEF) intended for approximation of multi-peaked light-ning current waveforms will be presented along with some of itsbasic properties. A general framework for estimating the parame-ters of the AEF using the Marquardt least-squares method(MLSM) for a waveform with an arbitrary (finite) number ofpeaks as well as a given charge transfer and specific energy willalso be described. This framework is used to find parameters forsome common single-peak wave-forms and some advantages anddisadvantages of the approach will be discussed.