This paper describes a cross-validation method to determine the appropriate weight with which dynamic constraints should be applied when estimating vocal tract shapes from speech. This data-dependent method can estimate the weighting without the need for separate prior knowledge of the source and noise statistics. The principles are first demonstrated on a simple one-dimensional system analogous to speech production. As the data here is synthetic, the statistics are known, and so the success of the method can be objectively assessed. Next, the same principles are extended to real speech to improve estimation of vocal tract shape trajectories.