Ni-rich Ni50.3Ti29.7Hf20 (at.%) high-temperature shape memory alloy (SMA) tubes were thermomechanically cycled under constant torques. Four loading configurations were examined that consisted of a series of ascending stresses (low-to-high stress from 0 to 500 MPa outer fiber shear stress), a series of descending stresses (high-to-low stress from 500 to 0 MPa), and a series of thermal cycles at a constant stress of 500 MPa, all using an upper cycle temperature (UCT) of 300 °C. The last configuration consisted of another series of ascending stress levels using a lesser UCT of 250 °C. It was found that the descending series trial stabilized the material response in fewer cycles than the other loading paths. Similarly, cycling at a constant stress of 500 MPa for approximately 100 cycles reached near stabilization (<0.05% residual strain accumulation). Transformation shear strains were the highest and most stable when cycled from lower-to-higher stresses (ascending series), reaching 5.78% at 400 MPa. Cycling to lesser UCTs of 250 °C (vs. 300 °C) resulted in the highest two-way shape memory effect (TWSME), measuring over 3.25%. This was attributed to the effect of retained martensite and any transformation dislocations that served to stabilize the TWSME at the lower UCT. Results of this study suggest that different training paths might be used, depending on actuator performance requirements, whether the principal need is to maximize transformation strain, maximize the two-way shear strain, or stabilize the response in fewer cycles.