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Invariant life-history theory has been used to identify parallels in life histories across diverse taxa. One important invariant life-history model predicts that, given simple assumptions and conditions, size-at-sex-change relative to maximum attainable body size (relative size-at-sex-change, RSSC) will be invariant across populations and species in sequential hermaphrodites. Even if there are broad species-wide limits to RSSC, populations could fine-tune RSSC to local conditions and, consequently, exhibit subtle but important differences in timing of sex change. Previous analyses of the invariant sex-change model have not explicitly considered the potential for meaningful differences in RSSC within the confines of a broader 'invariance'. Furthermore, these tests differ in their geographical and taxonomic scope, which could account for their conflicting conclusions. We test the model using several populations of three female-first sex-changing Caribbean parrotfish species. We first test for species-wide invariance using traditional log-log regressions and randomisation analyses of population-specific point estimates of RSSC. We then consider error around these point estimates, which is rarely incorporated into invariant analyses, to test for differences among populations in RSSC. Log-log regressions could not unequivocally diagnose invariance in RSSC across populations; randomisation tests identified an invariant RSSC in redband parrotfish only. Analyses that incorporated within-population variability in RSSC revealed differences among populations in timing of sex change, which were independent of geography for all species. While RSSC may be evolutionarily constrained (as in redband parrotfish), within these bounds the timing of sex change may vary among populations. This variability is overlooked by traditional invariant analyses and not predicted by the existing invariant model. [ABSTRACT FROM AUTHOR]