  The Lense-Thirring effect is currently being measured by means of a
combination of the orbital residuals of the nodes of LAGEOS and LAGEOS II and
the perigee of LAGEOS II. The total error is of the order of 20%. The most
insidious systematic error is due to the mismodelled even zonal harmonics of
the geopotential and amounts to 12.9%, according to EGM96 model. The role and
the importance of the LAGEOS--LAGEOS II Lense--Thirring experiment is
investigated. Using other suitable combinations with orbital elements of the
other existing laser-ranged satellites does not yield significative
improvements except for one combination including the nodes of LAGEOS, LAGEOS
II and Ajisai and the perigee of LAGEOS II. The related systematic error due to
the mismodelled even zonal part of the geopotential reduces to almost 10.7%.
