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We consider an ad-hoc network consisting of devices that try to gain access for transmission through a shared radio communication channel. We consider two randomized leader election protocols the first one is due to Nakanoand Olariu (2000); the second one is due to Cai, Lu and Wang (2003) and propose combinations which give us an improvement of both of them. We show that with discrete starting points of transmission, between which a station may choose in a non-uniform way, leads to a simple algorithm that substantially outperforms the previous techniques of resolving channel access problems. We provide methods to optimize values of parameters used.