Many common tasks compromise arm stability along specific directions. Such tasks can be completed only if the impedance of the arm is sufficient to compensate for the destabilizing effects of the task. During movement, it has been demonstrated that the direction of maximal arm stiffness, the static component of impedance, can be preferentially increased to compensate for directionally unstable environments. In contrast, numerous studies have shown that such control is not possible during postural tasks. It remains unknown if these findings represent a fundamental difference in the control of arm mechanics during posture and movement or an involuntary response to the destabilizing environments used in the movement studies but not yet tested during posture maintenance. Our goal was to quantify how arm impedance is adapted during postural tasks that compromise stability along specific directions. Our results demonstrate that impedance can be modulated to compensate for these instabilities during postural tasks but that the changes are modest relative to those previously reported during reaching. Our observed changes were primarily in the magnitude of end-point stiffness, but these were not sufficient to alter the direction of maximal stiffness. Furthermore, there were no substantial changes in the magnitude of end-point viscosity or inertia, suggesting that the primary change to arm impedance was a selective increase in stiffness to compensate for the destabilizing stiffness properties of the environment. We suggest that these modest changes provide an initial involuntary response to destabilizing environments prior to the larger changes that can be affected through voluntary interventions.