Measuring biodiversity requires empirical techniques to effectively estimate it from real data. The well-known underestimation of the number of species applies to low orders of diversity in general. I test nine estimators including three new ones on geometric and lognormal distributions that represent realistic, hyper-diverse communities. The best two estimators allow a good estimation of diversity of orders over 0.5, even when the sampling effort is low. I provide criteria to choose the estimator and the necessary code in the R package entropart.