A model reduction problem (MRP) is related to the control problem by use of a ‘ model quality index ’ which measures the performance of the higher-order system when the control is based upon a lower-order model. By truncating modal coordinates which have smaller sensitivity to the model quality index a first approximation to the MRP is obtained. Another approximation to the MRP is obtained by truncation of modal coordinates which have smaller sensitivities to the first term in the model quality index, called the ‘ cost of information ’. Several theorems relate the scalar measures of observability of each modal coordinate to the first-order sensitivity of the ‘ cost of information ’ and of the model quality index. A case study with a flexible spacecraft illustrates truncation on the basis of observability measures and controllability measures.