There have been a number of studies on mining candidate specifications from execution traces. Some extract specifications corresponding to value-based invariants, while others work on inferring ordering constraints. In this work, we merge our previous work on mining scenario-based specifications, extracting ordering constraints in the form of live sequence charts (LSC), a visual specification language, with Daikon, a tool for mining value-based invariants. The resulting approach strengthens the expressive power of the mined scenarios by enriching them with scenario-specific value-based invariants. The concept is illustrated using a preliminary case study on a real application.