Construction engineers compare as-built data against as-designed models for monitoring construction defects or changes. As laser scanners can collect 3D point clouds as as-built data in a few minutes, engineers start to compare point clouds against the as-designed model. Such comparison requires a reliable datamodel registration that precisely distinguishes data-model differences (e.g., displacements) from the well-matched parts. Previously developed registration methods have limitations on aligning two geometries with geometric differences. Target-based registration methods pose challenges of installing targets and ensuring their visibilities on job sites. Feature-based registration algorithms need engineers to manually set proper parameters to precisely reject data-model differences. Through the simulation of a progressive data-model registration process, this study characterizes a progressive 3D registration approach that can precisely reject data-model differences. Sensitivity analysis results of this approach in a case study show that this approach outperforms previous methods in terms of precision without losing substantial computational efficiency.