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The paper presents some preliminary results on distribution of pheromone evaporation values among ants in Ant System. Two cases are studied, one with uniform distribution of pheromone evaporation values among cities and other with Gaussian distribution. Experimental analysis is performed by comparing behavior of Ant System solving Traveling Salesman Problem. Minimum mean error found and number of near optimal solutions found are used as main indicators of Ant System performance evaluation. Pheromone evaporation coefficient values distribution showed very little to no impact on convergence speed. Preliminary experimental results confirm that by introducing a pheromone evaporation asymmetry, Ant System minimum mean error decreases up to 8 % and the number of near optimal solutions increases up to 25 % without sacrifice of convergence speed and without much change in complexity.