This study examines the effects of line simplification on the positional accuracy of linear features. The goal is to quantify the relation between the level of simplification and the degree of positional error, so that users can choose appropriate levels of simplification that will yield results meeting specific accuracy criteria. The study focuses on the Douglas-Peucker line simplification algorithm and examines both natural and anthropogenic features (streams and roads) derived from United States Geological Survey Digital Line Graphs. Results show that error can be modelled at an aggregate level using cumulative frequency curves and their confidence limits. This makes it possible to identify the level of simplification that eliminates the largest number of vertices while still attaining a specific positional accuracy standard. A simple implementation strategy is described in which an optimal level of simplification is identified and simplification is applied selectively for different lines. The study shows that management of simplification induced error is possible using simple tools well within the reach of GIS users.