When a tissue volume is sectioned, cells or other objects are cut into segments by the sectioning process. The Abercrombie and empirical methods count object segments in histological sections and then apply a correction formula to convert the segment count to object number. There has been considerable recent controversy over whether these methods should be abandoned (in favor of the disector). Although both methods appear unbiased as thought experiments on paper, regardless of variation in object size, shape, or orientation, in practice two problems are inherent in the segment-counting approach: the practical problem of lost caps and a conceptual flaw that becomes apparent only when a need for unbiased estimation of certain factors in the correction formulae is seriously addressed. The Abercrombie method is inevitably biased by lost caps, whereas in the empirical method, this potential bias can be avoided. In the Abercrombie formula, the relevant factor to be estimated (aside from section thickness) is H, mean object height in the axis perpendicular to the section plane, and in the empirical method, it is the ratio of segment number to object number. In both methods, the factor in question should be estimated from an unbiased sample of the total population of objects. But unbiased selection of a statistically adequate number of objects for this estimation constitutes an unbiased, statistically adequate count. Once this is done, there is no reason to complete the steps for estimation of the factor; the count in this specimen is finished. It is shown that the empirical method's serial section procedure can be used to estimate H. This estimate is more sensitive to lost caps than the Abercrombie equation, but, when the formula for H is substituted into the Abercrombie equation, the lost caps error disappears. However, this approach is useless, as making this substitution transforms the Abercrombie equation into the empirical method equation.