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This paper considers simultaneous fitting of multiple curves and surfaces to 3D measured data captured as part of a reverse engineering process, where constraints exist between the parameters of the curves or surfaces. Enforcing such constraints may be necessary (i) to produce models to sufficiently accurate tolerances for import into a CAD system, and (ii) to produce models which successfully reproduce regularities and symmetries required by engineering applications.The constraints to be satisfied may be determined manually, or more likely, by an automatic process. In the latter case, typically many more constraints are generated than can all be simultaneously satisfied. We present a new numerical method able to resolve conflicts between constraints.Secondly, reverse engineering generates large amounts of data. Constrained fitting methods are iterative in nature, and so an efficient method needs to restrict the amount of computation performed on each iteration. Our method achieves this through carefully constructed representations for objects and constraints, and approximations to distance functions.This paper describes our approach to constrained fitting, and illustrates its usefulness with some 2D and 3D examples taken from reverse engineering.