Significant systematic errors can result in precision surveying if the curvature of the earth is ignored in the adjustment of a survey network. The errors can become significant even for networks with very limited extent. An adjustment model for small-scale surveying networks such as precision three-dimensional metrology networks is presented in this paper which uses a local Cartesian coordinate system and applies curvature corrections to all the observations in a network. The adjustment model is useful especially for precise industrial metrology networks such as those established using real-time electronic theodolite systems.