Although many studies on the various ways of allocating credit among co-authors have brought into general recognition that different citation counting methods can result in quite different author rankings, studies on different author co-citation counting methods are still largely missing. This paper examines whether different co-citation counting methods produce different results in author co-citation analysis studies of the intellectual structure of research fields, and if so, in what ways they differ. Our results indicate that, with respect to the major specialties and how they relate to each other, the intellectual structures of the Information Science field identified through author co-citation analyses based on different co-citation counting methods are largely equivalent, but when it comes to detailed structure, results differ in a number of ways. In particular, classic first-author co-citation analysis appears to better represent the theoretical and methodological aspects of the field whereas all-author co-citation analysis favors more recent empirical studies, and picks out some tightly collaborative research groups or projects. We experiment with using meaningful diagonal values in a co-citation matrix rather than using statistically generated values, and observe favorable results. We also employ a new visualization technique for reporting the results of a classic author co-citation analysis, using a bipartite graph that represents all the information in the factor matrix of specialties and author loadings as author and factor vertices connected by edges with loadings as similarity-measure line values, laid out algorithmically in two dimensions.