The present study examines one of the fundamental aspects of author co-citation analysis (ACA): the way co-citation counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings are based, and we compare ACA results based on two different types of co-citation counting: on the one hand, the traditional type that only counts the first one among a cited work's authors, and on the other hand, a simplified approach to all-author co-citation counting that takes into account the first five authors of a cited work. Results indicate that the picture produced through this simplified all-author co-citation counting contains author groups that are more coherent, and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed. Variations of counting more than first authors are compared.