One of the basic advantages of the JET Core LIDAR Thomson Scattering system is the measuring of electron temperature Te and density ne profiles along the entire line of sight inside the torus. However, the spatial resolution is of the order of 12-15 cm and thus insufficient for resolving the narrow pedestal area, typically in the region of a few centimeters. Deconvolution technique has already been successfully applied to the LIDAR data. In spite of the improved resolution, the deconvolved Te and ne profiles remain extended outside the torus wall. In this work we are performing the next step to estimate the true shape of the Te pedestal from the Core LIDAR data as well as its basic parameters such as width, value and position. The method proposed is based on a preliminary transformation of the LIDAR profiles (step 3cm) to ones sampled with a new step of 1cm. Then, a convolution procedure with low pass filter characteristics (used in the deconvolution process) is applied to a specially designed model of the electron temperature profile with a variable pedestal function. An optimal least square fitting algorithm is applied to extract the best fit pedestal parameters at a preliminary chosen pedestal shape function. Results from the processing of a set of Core LIDAR data from different JET pulses for plasmas of high and low triangularity will be presented. The comparison with the High Resolution Thomson Scattering (HRTS) displays a good coincidence of the mean Te pedestal estimates within H-mode with best fits of HRTS pedestals. At this stage the method is effective for a set of 3-4 successive laser pulses (time resolution 0.75-1s). Possible upgrades of the LIDAR system with modern detectors and acquisition providing better signal-to-noise ratio, better spatial resolution and a higher sampling rate, and the improved method performance in this case will be discussed.