Several proposals have been launched under the new concept ‘integrative taxonomy’ to frame the future development of species discovery and description. We consider that some of those proposals have failed to be truly integrative, by not acknowledging the limitations of operational definitions of species, by defending some kinds of evidence as universally superior, by considering taxonomy to be irreconcilable with population genetics, or by ignoring that the heterogeneity of evolutionary processes often precludes full character congruence in species. Here we defend a taxonomy where species exist, but not in any particular way everyone might want them to exist; a taxonomy open to data and methods from population biology, phylogeography and phylogenetics, as well as any other discipline providing evidence about the origin and evolution of species. This new taxonomy embraces all the consequences of considering species as lineages of reproductive populations, encouraging the use of as many lines of evidence as possible, but without negating that a single line may also be the only one providing evidence for a particular species. Species cannot only be those reproductive populations showing broad character congruence and/or reproductive isolation, due to the different degrees of character congruence, as well as of reproductive isolation, that result from the heterogeneity of evolutionary processes causing lineage splitting and divergence. Also, any kind of character – and not only those established by tradition or fashion – is potentially relevant as evidence of lineage divergence. To conciliate the authors who only see species supported by broad character congruence as good species hypotheses, we explain how a hypothesis can gain corroboration using single or multiple lines of evidence, even in cases of discordance with other lines of evidence. Finally, we propose guidelines to identify the expected degree of stability (preliminary, unstable, and stable) of species hypotheses. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 101, 747–756.