Many states have adopted the Common Core State Standards (CCSS), which emphasize "deeper learning" skills, such as mastery of core academic content, critical thinking, problem-solving, and collaboration. But can the new tests being developed to align with the CCSS be used to promote deeper learning and high-quality classroom instruction? In response to this question, several key points are highlighted: (1) Testing can have a wide variety of effects on teachers' activities in the classroom, including changes in what is taught, how teachers allocate time and resources, and how teachers interact with students; (2) Tests of deeper learning are more likely to have an impact on classroom instruction if there are consequences for educators or students; however, attaching stakes that are too high can have negative effects on practice; and (3) The impact of new tests will be enhanced by policies that ensure that the tests mirror high-quality instruction, are part of a systemic change effort, and are accompanied by training and support to help teachers interpret and use test scores effectively. [This brief describes work done for RAND Education and documented in "New Assessments, Better Instruction? Designing Assessment Systems to Promote Instructional Improvement" (see ED561199).]