Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events E_{n}:=(f(X₁)+...+f(X_{n}))∈A_{n} where the summands are i.i.d. and E_{n} is a large or moderate deviation event. The approximation of the conditional density of the real r.v's X_{i} 's , for 1≤i≤k_{n} with repect to E_{n} on long runs, when k_{n}/n→1, is handled. The maximal value of k compatible with a given accuracy is discussed; algorithms and simulated results are presented.