The Multipoint Expected Improvement criterion (or q-EI) has recently been studied in batch-sequential Bayesian Optimization. This paper deals with the new way of computing q-EI, without usingMonte-Carlo simulations, through a new closed form formula. The latter allows a very fast computation of q-EI for reasonably low values of q (typically, less than 10). New parallel kriging-based optimization strategies, tested on various toy examples, show promising results.