Typically, a video rate control algorithm minimizes the average distortion (denoted as MINAVE) at the cost of large temporal quality variation, especially for videos with high motion and frequent scene changes. To alleviate the negative effect on subjective video quality, another criterion that restricts a small amount of quality variation among adjacent frames is preferred for practical applications. As pointed out by [20], although some existing proposals can produce consistent quality videos, they often fail to fully utilize the available bits to minimize the global total distortion. In this paper, we would like to achieve the triple goal of consistent quality video, minimizing the total distortion, and meeting the bit budget strictly all at the same time on the interframe dependent coding structure. Two approaches are taken to accomplish this goal. In the first algorithm, a trellis-based framework is proposed. One of our contributions is to derive an equivalent condition between the distortion minimization problem and the budget minimization problem. Second, our trellis state (tree node) is defined in terms of distortion, which facilitates the consistent quality control. Third, by adjusting one key parameter in our algorithm, a solution in between the MINAVE and the constant quality criteria can be obtained. The second approach is to combine the Lagrange multipliers method together with the consistent quality control. The PSNR performance is degraded slightly but the computational complexity is significantly reduced.Simulation results show that both our approaches produce a much smaller PSNR variation at a slight average PSNR loss as compared to the MPEG JM rate control. When they are compared to the other consistent quality proposals, only the proposed algorithms can strictly meet the target bit budget requirement (no more, no less) and produce the largest average PSNR at a small PSNR variation.