In this talk we describe new techniques we proposed for estimating the probability that the sum of nonnegative independent and identically distributed random variables falls below a given threshold, in the rare event case, when this probability is extremely small. We discuss how to improve the classical exponential twisting technique, by means of appropriante Important Sampling schemes. Specifically, we describe how using a well-chosen Gamma distribution provides such an improvement. The obtained improvements are illustrated by several numerical experimentations.