  This paper presents an improved result on the negative-binomial Monte Carlo
technique analyzed in a previous paper for the estimation of an unknown
probability p. Specifically, the confidence level associated to a relative
interval [p/\mu_2, p\mu_1], with \mu_1, \mu_2 > 1, is proved to exceed its
asymptotic value for a broader range of intervals than that given in the
referred paper, and for any value of p. This extends the applicability of the
estimator, relaxing the conditions that guarantee a given confidence level.
