Crystallographic orientation and cooling rate dependences of the shape memory effect and pseudoelasticity are reported for CoNiAl alloy single crystals oriented along the [001], [110] and [123] directions. Phase transformation response, pseudoelasticity and two-way shape memory effect were investigated through thermo-mechanical experiments. The experimentally determined transformation strains exceeding the theoretical values in the [110] orientation single crystals are attributed to the additional contribution from the detwinning strain. High cooling rates (oil and water quenching) were found to lead to a lower γ-phase volume fraction that resulted in higher shape memory strains under low external stresses. Moreover, the [001] oriented single crystals demonstrated perfect pseudoelasticity (up to 4.3% strain), a large pseudoelastic window (>140 °C), high resistance to dislocation slip and small thermal hysteresis. The existence of detwinning, easy reorientation of favorable variants under low external stresses and significant fully recoverable strains have important implications regarding the magnetic field-induced shape changes in this class of alloys.