The precise geometric levelling has been the main method for establishing height reference systems since the eighteenth century. Despite evaluating the methodology of measurements, levelling equipment, and the knowledge about the systematic effect of some natural processes, some systematic errors in the levelling data processing are still used in the geodetic practice. Such a systematic data processing error uses the mean of the measured line elevations in opposite directions. A newly revealed distribution Cv(n) gives the probability that the mean of n observations has the least true error than each of these n observations. The maximum value of the Cv(n) probability density function is in the case of the uniformly distributed data and n=3. In this case, Cv(n=3) < 0.50. The common case for the precise levelling is a line elevation to be measured twice, i.e., n=2. Then, the probability Cv(n=2) < 0.33. Consequently, using original values of the measured line elevations as initial data in an adjustment of a levelling network is expected to give better results than their means. The expected increase in accuracy is estimated to be twice. To test this theory, we readjusted the Third Levelling of Bulgaria network /1975-1984/ by selecting one of the two measured line elevations by a greedy algorithm. Comparison of the samples of benchmark height standard errors obtained by applying only the original measurements on the one hand, and the means of the other, shows the superiority of the proposed approach. Comparison of the means by t-test confirms this conclusion at a significance level higher than 99.99%. Comparison of the variations of the benchmark standard error samples rejected the null hypothesis of the sample variance equality at a significance level higher than 99%. In addition, the analysis of the differences between the adjusted benchmark heights reveals a systematic inclination of the classical adjusted variant in the Southeast-Northwest direction greater than +0.10 mm/km. The last value is close to the estimated systematic error of the Third Levelling of Bulgaria

Height reference systems; jackknife; entropy; probability; precise levelling