Microtubule diversity, arising from the utilization of various isoforms and posttranslational modifications of tubulin, affects many cellular processes, including the assembly and motility cilia and flagella. However, it is not known whether microtubule diversity directly regulates the activity of the axonemal dyneins, the motors that drive the beating of cilia. To test this possibility, we asked whether in vitro acetylation or deacetylation of α-tubulin's lysine 40 (K40), which is an important posttranslational modification of tubulin within the lumen of microtubules, can influence the activity of outer arm axonemal dynein in motility assays using purified proteins. Additionally, we asked whether proteolytic cleavage of α- and- β-tubulin's C-terminal tails (CTT), which are unstructured regions on the outside of the microtubule lattice and are the location of the detyrosination, polyglutamylation, and polyglycylation modifications as well as most of the genetic diversity between tubulins, regulate dynein's motility. By quantifying the motility with displacement-weighted velocity analysis, we found that both K40 acetylation CTT cleavage increase the motility of axonemal dynein. Our mathematical modeling further suggests that the increase in motility is due to an increase in the power stroke speed of dynein in both cases. These results show that axonemal dynein directly deciphers the tubulin code; specifically luminal acetylation of lysine 40 on α-tubulin increases the motility of dynein on the exterior of the microtubule, and CTTs, and their associated post-translational modifications, tend to decrease motility of dynein. This work has implications on allostery between the microtubule lumen and the external surface, the effect of post-translational modifications on molecular motors and microtubule associated proteins, and the regulation of the eukaryotic ciliary beat.