Lognormal kriging was developed early in geostatistics to take account of the often seen skewed distribution of the experimental mining data. Intuitively, taking the distribution of the data into account should lead to a better local estimate than that which would have been obtained when it is ignored. In practice however, the results obtained are sometimes disappointing. This paper tries to explain why this is so from the behavior of the lognormal kriging estimator. The estimator is shown to respect certain unbiasedness properties when considering the whole working field using the regression curve and its confidence interval for both simple or ordinary kriging. When examined locally, however, the estimator presents a behavior that is neither expected nor intuitive. These results lead to the question: is the theoretically correct lognormal kriging estimator suited to the practical problem of local estimation?