A variety of hemodynamic wall parameters (HWP) has been proposed over the years to quantify hemodynamic disturbances as potential predictors or indicators of vascular wall dysfunction. The aim of this study was to determine whether some of these might, for practical purposes, be considered redundant. Image-based computational fluid dynamics simulations were carried out for $N=50$ normal carotid bifurcations reconstructed from magnetic resonance imaging. Pairwise Spearman correlation analysis was performed for HWP quantifying wall shear stress magnitudes, spatial and temporal gradients, and harmonic contents. These were based on the spatial distributions of each HWP and, separately, the amount of the surface exposed to each HWP beyond an objectively-defined threshold. Strong and significant correlations were found among the related trio of time-averaged wall shear stress magnitude (TAWSS), oscillatory shear index (OSI), and relative residence time (RRT). Wall shear stress spatial gradient (WSSG) was strongly and positively correlated with TAWSS. Correlations with Himburg and Friedman’s dominant harmonic (DH) parameter were found to depend on how the wall shear stress magnitude was defined in the presence of flow reversals. Many of the proposed HWP were found to provide essentially the same information about disturbed flow at the normal carotid bifurcation. RRT is recommended as a robust single metric of low and oscillating shear. On the other hand, gradient-based HWP may be of limited utility in light of possible redundancies with other HWP, and practical challenges in their measurement. Further investigations are encouraged before these findings should be extrapolated to other vascular territories.