International audienceWe consider some practical issues of the determination of the b-value of sequences of magnitudes with the bootstrap method for short series of length L and various quantization levels Dm of the magnitude. Preliminary Monte Carlo tests performed with Dm ¼ 0 demonstrate the superiority of the maximum likelihood estimator bMLE, and the inconsistency of the, yet often used, bLR estimator defined as the least-squares slope of the experimental Gutenberg-Richter curve. The Monte Carlo tests are also applied to an estimator, bKS, which minimizes the Kolmogorov-Smirnov distance between the cumulative distribution of magnitudes and a power-law model. Monte Carlo tests of discrete versions of the bMLE and bKS estimators are done for Dm ¼ f0:1; 0:2; 0:3g and used as reference to evaluate the performance of the bootstrap determination of b. We show that all estimators provide b estimates within 10 % error for L C 100 and if a large number, n = 2 9 105, of bootstrapped sample series is used. A resolution test done with Dm ¼ 0:1 reveals that a clear distinction between b = 0.8, 1.0, and 1.2 is obtained if L= 200