The superior temporal sulcus (STS) is an important region for speech comprehension. The greater language network is known to exhibit asymmetries in both structure and function, and consistent with that theory are reports of STS structural asymmetry in MRI-based, morphological measures such as mean thickness and sulcal depth. However, it is not known how these individual STS structural asymmetries relate to each other, or how they interact with the broader language asymmetry that manifests in other brain regions. In this study, we assess the interrelations of STS asymmetries in the human brain in vivo, using four independent datasets to validate our findings. For morphological measurements, we identify STS laterality effects consistent between our datasets and with the literature: leftward for surface area, and rightward for sulcal depth and mean thickness. We then add two more measurements of STS asymmetry: in T1, a quantitative index of the tissue’s underlying biophysical properties; and in the projections to the STS from the arcuate fasciculus, a left-lateralized white-matter bundle that connects temporal regions (including STS) with frontal regions (including Broca’s area). For these two new measurements, we identify no effect for T1 and a leftward effect for arcuate projections. We then test for correlations between these STS asymmetries, and find associations mainly between measurements of the same type (e.g., two morphological measurements). Finally, we ask if STS asymmetry is preferentially related to Broca asymmetry, as these are both important language regions and connected via the arcuate fasciculus. Using a linear model with cross-validation, we find that random regions are as successful as Broca’s area in predicting STS, and no indication of a hypothesized leftward asymmetry. We conclude that although these different STS asymmetries are robust across datasets, they are not trivially related to each other, suggesting different biological or imaging sources for different aspects of STS lateralities.