The joints of the hand provide 24 mechanical degrees of freedom. Yet 2–7 principal components (PCs) account for 80–95% of the variance in hand joint motion during tasks that vary from grasping to finger spelling. Such findings have led to the hypothesis that the brain may simplify operation of the hand by preferentially controlling PCs. We tested this hypothesis using data recorded from the primary motor cortex (M1) during individuated finger and wrist movements. Principal component analysis (PCA) of the simultaneous position of the five digits and the wrist showed relatively consistent kinematic synergies across recording sessions in two monkeys. The first three PCs typically accounted for 85% of the variance. Cross-correlations then were calculated between the firing rate of single neurons and the simultaneous flexion/extension motion of each of the five digits and the wrist, as well as with each of their six PCs. For each neuron, we then compared the maximal absolute value of the cross-correlations (MAXC) achieved with the motion of any digit or the wrist to the MAXC achieved with motion along any PC axis. The MAXC with a digit and the MAXC with a PC were themselves highly correlated across neurons. A minority of neurons correlated more strongly with a PC than with any digit. But for the populations of neurons sampled from each of two subjects, MAXCs with digits were slightly but significantly higher than those with PCs. We therefore reject the hypothesis that M1 neurons preferentially control PCs of hand motion. We cannot exclude the possibility that M1 neurons might control kinematic synergies identified using linear or non-linear methods other than PCA. We consider it more likely, however, that neurons in other centers of the motor system – such as the pontomedullary reticular formation and the spinal gray matter – drive synergies of movement and/or muscles, which M1 neurons act to fractionate in producing individuated finger and wrist movements.