It has been proposed that the pollical phalangeal length proportions of the Neandertals provided them with a greater mechanical advantage relative to recent humans for their pollical flexor muscles in power grips across the interphalangeal (IP) joint at the expense of the mechanical advantage of those pollical flexor muscles in precision grips at the finger tip. To test these related hypotheses, we compared the pollical load arm dimensions (phalanx lengths) to power arm dimensions (dorsopalmar articular heights) for the European and Near Eastern Neandertals and for European and Amerindian samples of recent humans. It was found, initially, that the proximal articular height of the pollical distal phalanx is a poor predictor of the power arm at the IP articulation, even though the proximal articular height of the pollical proximal phalanx was an adequate indicator of the power arm size at the metacarpophalangeal (MCP) joint. In addition, differences in distal pollical ulnar deviation at the IP joint appeared to make little difference in the mechanical advantage comparisons. More importantly, the relative shortness of Neandertal proximal pollical phalanges and the relative lengthening of their distal pollical phalanges was confirmed, and it was determined that, despite some minor differences in articular dimensions between Neandertals and recent humans, these pollical phalangeal length contrasts translated into significant differences in mechanical advantages for the flexor muscles across the MCP and IP articulations.