Experimental studies of a high- plasma in a long solenoid of the axisymmetric mirror trap AMBAL-M are being continued. In order to increase the density of the initial warm plasma generated by a plasma source, additional gas puffing was used. Optimization of gas puffing through a gas-box and reduction of magnetic field in the solenoid aimed at enhancement were performed. Another way of increasing consists in forming a small local mirror-trap in the solenoid where the plasma volume is much smaller than that of the whole solenoid plasma, and it is easier to achieve high -values. A preliminary result on the local-mirror-trap experiment is presented. Further steps on increase in the solenoid are proposed and discussed.