Approximate addition is a technique to trade off energy consumption and output quality in error-tolerant applications. In prior art, bit truncation has been explored as a lever to dynamically trade off energy and quality. In this brief, an innovative bit truncation strategy is proposed to achieve more graceful quality degradation compared to state of-the-art truncation schemes. This translates into energy reduction at a given quality target. When applied to a ripple-carry adder, the proposed bit truncation approach improves quality by up to 8.5 dB in terms of peak signal-to-noise ratio, compared to traditional bit truncation. As a case study, the proposed approach was applied to a discrete cosine transform engine. In comparison with prior art, the proposed approach reduces energy by 20%, at insignificant delay and silicon area overhead.