This study considers and evaluates the implementation of two strategies to improve student engagement with assessment -- the provision of exemplars in conjunction with rubrics, and student co-construction of rubrics -- as, respectively, a supplement and an alternative to teacher-designed rubrics. It follows our 2016 finding that teacher-designed rubrics, alone, may not provide students with sufficient clarity and transparency about assessment tasks either before beginning the task or upon receiving feedback. The use of exemplars to support rubrics was found to be the more effective strategy, although the idea of student rubric co-construction was found to have some promise. A key contribution of this paper is that it suggests the importance of the affective dimensions of students' engagement with assessment.