Sensorimotor impairments after limb amputation impose a threat to stability. Commonly described strategies for maintaining stability are the posture first strategy (prioritization of balance) and posture second strategy (prioritization of concurrent tasks). The existence of these strategies was examined in 13 below-knee prosthesis users and 15 controls during dual-task standing under increasing postural and cognitive challenge by evaluating path length, 95% sway area, and anterior–posterior and medial–lateral amplitudes of the center of pressure. The subjects stood on two force platforms under usual (hard surface/eyes open) and difficult (soft surface/eyes closed) conditions, first alone and while performing a cognitive task without and then with instruction on cognitive prioritization. During standing alone, sway was not significantly different between groups. After adding the cognitive task without prioritization instruction, prosthesis users increased sway more under the dual-task than single-task standing (p ≤ 0.028) during both usual and difficult conditions, favoring the posture second strategy. Controls, however, reduced dual-task sway under a greater postural challenge (p ≤ 0.017), suggesting the posture first strategy. With prioritization of the cognitive task, sway was unchanged or reduced in prosthesis users, suggesting departure from the posture second strategy, whereas controls maintained the posture first strategy. Individual analysis of dual tasking revealed that greater postural demand in controls and greater cognitive challenge in prosthesis users led to both reduced sway and improved cognitive performance, suggesting cognitive–motor facilitation. Thus, activation of additional resources through increased alertness, rather than posture prioritization, may explain dual-task performance in both prosthesis users and controls under increasing postural and cognitive challenge.