Adjustable-prescription orthodontic brackets that include a bracket body, a repositionable core that defines an archwire slot, and a core positioning assembly. The bracket body defines a core receptacle into which the core is received and selectively moved within a plurality of prescriptive orientations. The core positioning assembly is selectively transitioned between a disengaged configuration, in which the core positioning assembly permits movement of the core relative to the bracket body within the plurality of prescriptive orientations, and an engaged configuration, in which the core positioning assembly retains the core at the selected prescriptive orientation. The core positioning assembly includes a core clamp with a core engagement surface configured to be selectively engaged with the core, and an actuator configured to selectively secure the core clamp in engagement with the core to retain the core at the selected prescriptive orientation.