Recent tests of adding observations to improve individual forecasts have shown a mix of positive, negative, and neutral results. In this study, the influence of added observations on analysis and forecast errors is explored in idealized systems. The primary system studied is a three-dimensional simulated observing and forecasting system that includes a quasi-geostrophic forecast model and a three-dimensional variational data-assimilation system. In this simulated system, adding observations generally improves analyses and often improves 12-hour forecasts. Even with perfect observational data and a perfect forecast model, however, there is a non-negligible risk that adding observations will degrade analyses, and a significant risk that assimilated added observations will degrade forecasts on a time-scale of one or several days. To illustrate several general principles that help interpret the results, several experiments are performed with low-dimensional data-assimilation systems; the results demonstrate that the risk of analysis degradation is inherent in statistical data assimilation. Experiments are also performed with a low-dimensional forecast model, demonstrating that the risk of forecast degradation is inherent in prediction systems with sensitivity to small errors in initial conditions. Although degradations cannot be avoided, several circumstances are identified in which adding observations is less likely to degrade analyses and forecasts and on average improves analyses and forecasts by a larger amount. Copyright © 2002 Royal Meteorological Society.