A method of making a casting having an internal passage involves the steps of forming a core having an external surface configured to form the passage in the casting and having a plurality of integrally formed protrusions extending from the external surface at stressed regions thereof (e.g., thermally stressed regions) prone to be distorted from a master core configuration, and positioning the core in a pattern molding cavity by engagement of the protrusions with rigid walls defining the molding cavity such that the core is conformed substantially to a predetermined and/or empirically determined relationship between the master core configuration and the molding cavity as if the core corresponded to the master core configuration. A fugitive pattern corresponding to the casting to be formed is then molded about the external surface of the core while the core is supported in the aforementioned relationship relative to the molding cavity, whereby the wall thickness of the pattern is controlled about the core. A ceramic shell mold is then invested about the pattern and core such that the protrusions can engage the mold in the event of core movement during subsequent steps.