It is known that video quality fluctuation plays a major negative role on visual perception. In [1], we derived close-form approximations to mimic the highly nonlinear ratedistortion (R-D) and distortion-quantization (D-Q) relationships. Using the two close forms, we can allocate the bit rate at the frame-level rather easily so long as a target distortion for each frame is established. In [1], we set up the target distortion at each frame using a hypothesis that maintaining constant distortion across frames would ease video quality fluctuation. The extensive experiments showed the constant-distortion bit allocation (CDBA) scheme proposed in [11 delivered much smoother video quality than the conventional constant bit allocation (CBA) scheme. However, maintaining constant distortion is about the same as maintaining constant Peak-Signal-to-Noise-Ratio (PSNR). In scene changes, the picture energy often dramatically changes that could generate significantly different Signal-to-Noise-Ratio (SNR) if constant distortion or constant PSNR is maintained. Although computationally more complex, SNR does represent a more objective measure than PSNR in assessment of picture/video quality. In the paper, we consolidate a constant SNR bit allocation (CSNRBA) scheme that attempts to maintain constant SNR throughout the video frames. Extensive experiments show that the CSNRBA scheme provides smooth video quality in terms of natural colors and sharp objects and silhouettes significantly better than both the CBA and CDBA schemes.