In our prior work, we presented an algorithm called Largest Magnitude Coefficient Selection (LMCS) for realizing the signal-to-noise-ratio (SNR) scaling of an already encoded video object to an alternate (lower) rate (higher) distortion level. We showed that LMCS retains semantically important image features and successfully avoids the common artifacts of blur and ringing noise. However, it suffers from a significant coding inefficiency problem. In this paper, we first identify the mechanisms which lead to the problem, and consequently present a novel technique called Pivoting in order to alleviate it. The comparison of the resulting algorithm, LMCS-Pivot, against the conventional SNR scaling techniques demonstrates its effectiveness according to both objective and subjective performance measures.