The walls of Structure J at the Zapotec centre of Monte Albán incorporate monuments, probably carved during the Pe ceramic phase (300–100 bc), bearing distinctively formatted hieroglyphic inscriptions. Alfonso Caso suggested that hieroglyphic compounds on those monuments name regions conquered by Monte Albán. Many scholars accept an elaboration by Joyce Marcus on this proposal—that some of those compounds denote identifiable places outside the Valley of Oaxaca—and see the inscriptions as evidence for the territorial extent of an expansionist, Monte Albán-centred empire in the Late to Terminal Formative periods (300 bc–ad 200). This paper argues that Marcus’ proposed decipherments are implausible because they are structurally inconsistent with one another and with Zapotec scribal conventions for recording toponyms in other inscriptions. The Structure J texts remain undeciphered. Therefore they cannot now serve as evidence for the nature and reach of the Monte Albán polity, and generalizations about state formation that relied on Marcus’ readings need to be reconsidered.