This article is devoted to the determination of Earth' Orientation Parameters (EOP) from reprocessing of the Laser ranging observations of the specially designed satellites. These are laser geodynamics satellites Lageos, Etalon and Low Earth Orbiters Lares, Ajisai, Starlette, Stella. New software was created by the author and a new approach was proposed to analyze each model of geodynamics phenomena, transformation or process first tests separately and only then is included into the package. Main attention was paid to the analysis of the possibility to use Laser Ranging data to Low Earth Orbiters for EOP determination. It was shown that despite the much lower Lares' orbit (height is 700 km) than the Lageos' orbit (7000 km) the resulting EOP series from Lares data have in general the same precision. It was achieved by new software and new author approach to the study of the models. Final EOP data sets at the same time were computed by combination of raw EOPs from each satellite or from the combination of the conditional equations. In the latter case the precision of the final solution is l0—l5 % better. It allows us to recommend Low Earth orbiters for geodynamics on a permanent basis.