The baseline positron source of CLIC has been optimised for the 3 TeV c.o.m. energy. Now the first stage of the CLIC is proposed to be at 380 GeV. Recently, the positron transmission efficiency from the tungsten target to the damping rings injection has been improved by 2.5 times. This opened the possibility for an optimisation of the whole positron source, comprising the injector linacs, aimed at improving its performance and its overall power efficiency. In this paper the key parameters of the positron source, which include the current and the energy of the primary electron beam, the thickness of the crystal and amorphous tungsten targets, the distance between the two targets, the adiabatic matching device (AMD) and pre-injector linacs, are optimized to improve the overall power efficiency