Objective When a stroke damages the corticospinal tract (CST), it has been hypothesized that the motor system switches to using the corticoreticulospinal tract (CRST) resulting in abnormal arm synergies. Is use of these tracts mutually exclusive, or can the motor system spontaneously switch between them depending on the type of movement it wants to make? If the motor system can share control at will, then people with a rudimentary ability to make dexterous movements should be able to perform synergistic arm movements as well. Methods We analyzed clinical assessments of 319 persons’ abilities to perform “out-of-synergy” and “in-synergy” arm movements after chronic stroke using the Upper Extremity Fugl-Meyer (UEFM) scale. Results We identified a moderate range of arm impairment (UEFM = ~30-40) where subjects had a rudimentary ability to make out-of-synergy (~23%-50% on the out-of-synergy score) and dexterous hand movements (~3-10 blocks on Box and Blocks Test). Below this range persons could perform in-synergy but not out-of-synergy or dexterous movements. In the moderate range, however, scoring better on out-of-synergy movements correlated with scoring worse on in-synergy movements ( P = .001, r ≈ −0.6). Conclusion Rudimentary dexterity corresponded with reduced ability to move the arm in-synergy. This finding supports the idea that CST and CRST compete and has implications for rehabilitation therapy.