Power consumption of digital systems may increase significantly during testing. In this paper, systems equipped with a scan-based built-in self-test like the STUMPS architecture are analyzed, the modules and modes with the highest power consumption are identified, and design modifications to reduce power consumption are proposed. The design modifications include some gating logic for masking the scan path activity during shifting, and the synthesis of additional logic for suppressing random patterns which do not contribute to increase the fault coverage. These design changes reduce power consumption during BIST by several orders of magnitude, at very low cost in terms of area and performance.