We describe and evaluate a robust method for compressive sensing MRI reconstruction using an iterative soft thresholding framework that is data-driven, so that no tuning of free parameters is required. The approach described here combines a Nesterov type optimal gradient scheme for iterative update along with standard wavelet-based adaptive denoising methods, resulting in a leaner implementation compared with the nonlinear conjugate gradient method. Tests with T2 weighted brain data and vascular 3D phase contrast data show that the image quality of reconstructions is comparable with those from an empirically tuned nonlinear conjugate gradient approach. Statistical analysis of image quality scores for multiple datasets indicates that the iterative soft thresholding approach as presented here may improve the robustness of the reconstruction and the image quality, when compared with nonlinear conjugate gradient that requires manual tuning for each dataset. A data-driven approach as illustrated in this article should improve future clinical applicability of compressive sensing image reconstruction. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc.