We show with simulation experiments that closed-loop phase- diversity can be used without numerical guard-bands for wavefront sensing of low-order wavefronts from extended objects using broad-band filters. This may allow real-time correction at high bandwidth for certain applications. We also present a proper maximum likelihood treatment of Shack- Hartmann data, which includes an imaging model to extract curvature information from the lenslet images. We demonstrate by simple simulations that this approach should allow higher-order wavefront information to be extracted than with traditional Shack-Hartmann wavefront sensing for a given number of lenslets.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.