Causal analysis of covariance structures through structural equation modeling represents an indispensable tool for theory development and theory testing. In order to decide on whether to accept or reject a theoretical model, researchers rely on goodness-of-fit indices. However, the majority of currently used fit indices are global, that is, they are a function of the fit of both the measurement and the structural model. As has been shown by McDonald and Ho (2002) and O'Boyle and Williams (2011), this often leads researchers to erroneously accept misspecified models because good fit of the measurement model masks bad fit of the structural model. This study aims to provide alternative, more accurate fit indices. Two general frameworks for fit indices that rely on fit of the structural model only were developed, testing James' et al. (1982) condition nine and ten. Path-related fit indices were derived from the two frameworks and their performance under several different cutoff values was tested in a simulation of six population models. Their performance was compared to the performance of four of the most popular and widely used global fit indices CFI, RMSEA, TLI, and SRMR. Results show that all newly developed path-related fit indices are considerably more accurate in rejecting even slightly misspecified models than any of the global fit indices. Recommendations and implications for theory and practice are discussed.