In a cellular radio system a limited number of channels are available and neighbouring cells may not be allocated the same channel simultaneously because of the possibility of interference. Under heavy traffic, therefore, the average rate of losing calls may be reduced if certain calls are rejected as a matter of policy because of the potential inference they may cause. A fixed channel assignment policy is one in which each cell is allocated a fixed set of channels, this set typically being made smaller for cells likely to cause most interference. Sufficient conditions are found for the optimality of fixed channel assignment policies for a variety of layouts, and optimal and ‘good' policies are found in a number of other cases.