Postural sway was assessed [via center of pressure (COP) 95% elliptical area (EA), path length (PL), normalized path length (PL(n)) and sample entropy (SEn)] in four conditions of bipedal upright stance [compliant (Foam) vs. non-compliant (Hard) with eyes-open (EO) vs. eyes-closed (EC)] prior to, and immediately following, a six-week balance training intervention in a group of healthy adults (N = 26). The intervention was comprised of nine exercises progressed in difficulty based on the subjective assessments of individual competency. Results showed that EA and PL were increased, while PL(n) and SEn were decreased, in EC and Foam stance conditions (collapsed across effects of balance training). Interpretations were that restricted vision and a compliant surface represented constraints to postural control that caused increases in the amount (PL) and area (EA) of sway, but decreases in its coordinative twisting/turning (PL(n)) and temporal complexity (SEn). It was argued that these changes might represent compensatory adaptations in effort to maintain postural control given the demands of the imposed constraints. Balance training caused no change to EA, but did result in decreased PL, PL(n), and SEn for stance conditions performed on the Foam (either EO or EC). These changes were interpreted to reflect improved postural control, potentially through the learned adoption of a more deterministic postural control strategy that is uniquely defined by the constraints imposed on upright stance by the compliant surface.