Our basic idea of generating random benchmark circuits, i.e., not generating them directly but applying random transformations to initial circuits was presented at DAC'94. In this paper we make the two major improvements towards the goal of random benchmarking: i.e., increasing the generality, the naturality, the security of random circuits: One is controlling fan-ins of logic gates in the random circuits, and the other is producing the initial circuit also at random but under some control of its on-set size and complexity. Experimental data claiming merits of those improvements are also given.