The low success and retention rates in CS1 are well-known problems. This paper discusses the importance of assessment and grading strategies when dealing with those problems, as both are seen as fundamentally important for improving student motivation and learning along the whole course. More specifically, the paper presents a set of criteria and a set of techniques that should be considered and balanced when defining the assessment and grading methodology. Both sets were identified based on the literature and on the author's experience teaching several introductory programming courses, with traditional high attrition and failure rates, in a small non-elite school. Yet, probably they are applicable and useful for defining the assessment and grading schemes for any CS1 course or even other subject matters. The paper also aims to provide a basis for the discussion of the right balance between student learning, fraud minimization, and available resources. The paper ends with a proposal for a concrete methodology for assessment and grading that has been refined over the last three years.