In an effort to reduce failure and attrition rates and to increase on-time program completion and graduation rates, many schools are adopting a policy of assigning minimum grades. While justifications supporting the policy are often mathematical in nature, some proponents also claim the practice works to keep students motivated, hopeful, confident and optimistic. This paper explores these claims by comparing the stated reasons for grading practices and policies against several theories of learning and the secondary effects grades have on students. Key concepts from the models of achievement motivation, locus of control and self-efficacy, as well as consideration of the nature of intrinsic and extrinsic motivation, lead to conclusions that there may be certain sub-populations of students who could benefit greatly from minimum grading practices and policies, particularly in certain (“high-risk”) courses and subject-matters. Ways to identify these students, courses and subject matters are presented and discussed, as are the general outlines of the formal exploratory and confirmatory studies that are needed to clarify and more precisely answer the several questions about minimum grading policies identified in this paper.