The Neyman-Pearson theory suffers from two well-known deficiencies: the asymmetric role of size and power and the coarse dichotomic decision a test yields. To overcome these drawbacks, Rüger (1979, 1980) and Wassmer (1993) developed Niveau Profile Tests (Profile Tests). In principle, these tests succeeded. For composite hypotheses, however, they do not yield the intended refinement. For one-side hypotheses, even if there are indifference regions between them, those tests are capable of three decisions only: “reject the hypothesis”, “do not reject the hypothesis” and “remain indifferent”. Therefore, a revision seems indicated. The revision aims at constructing tests which are always capable of more decisions, even if the hypotheses are composite. These tests will be called “Cumulative Niveau Profile Tests”. The article contains the method of constructing those tests, criteria for comparison and a definition of optimality. Existence and uniqueness theorems are formulated.