Multi-dimensional rate control schemes, which jointly adjust two or three coding parameters, have been recently proposed to achieve a target bit rate while maximizing some objective measures of video quality. The objective measures used in these schemes are the peak signal-to-noise ratio (PSNR) or the sum of absolute errors (SAE) of the decoded video. These objective measures of quality may differ substantially from subjective quality, especially when changes of spatial resolution and frame rate are involved. The proposed schemes are, therefore, not optimal in terms of human visual perception. We have investigated the impact on subjective video quality of the three coding parameters: spatial resolution, frame rate, and quantization parameter (QP). To this end, we have conducted two experiments using the H.263+ codec and five video sequences. In Experiment 1, we evaluated the impact of jointly adjusting QP and frame rate on subjective quality and bit rate. In Experiment 2, we evaluated the impact of jointly adjusting QP and spatial resolution. From these experiments, we suggest several general rules and guidelines that can be useful in the design of an optimal multi-dimensional rate control scheme. The experiments also show that PSNR and SAE do not adequately reflect perceived video quality when changes in spatial resolution and frame rate are involved, and are therefore not adequate for assessing quality in a multi-dimensional rate control scheme. This paper describes the method and results of the investigation.