Previous work by the authors developed algorithms for simplifying the structure of a lumped dynamic system model and reducing its order. This paper extends this previous work to enable simultaneous model structure and order reduction. Specifically, it introduces a new energy-based metric to evaluate the relative importance of energetic connections in a model. This metric (1) accounts for correlations between energy flow patterns in a model using the Karhunen-Loève expansion; (2) examines all energetic connections in a model, thereby assessing the relative importance of both energetic components and their interactions, and enabling both order and structural reduction; and (3) is realization-preserving, in the sense of not requiring a state transformation. A reduction scheme based on this metric is presented and illustrated using a simple example.