Forming the image from a CAT scan and taking the blur out of vacation pictures are problems that are ill-posed. By definition, small changes in the data to an ill-posed problem make arbitrarily large changes in the solution. How can we hope to solve such problems when data are noisy and computer arithmetic is inexact? In this talk we discuss the use of calibration data, side conditions, and bias constraints to improve the quality of solutions and our confidence in the results. Some of this work is joint with Julianne Chung, Matthias Chung, James Nagy, and Bert Rust.