This paper is a continuation of the work begun in "Mathematical Foundations of Classical Test Theory: An Axiomatic Approach, (RB-62-17). The notions of subtest and item (non-0-1 as well as 0-1) are defined in terms of the concepts introduced in RB-62-17. The bulk of the paper is concerned with the determination, based on a single trial, of lower bounds to the coefficient of reliability of a test. Six such bounds are established and compared. A short section on bounds to validity coefficients is included. The paper concludes with a somewhat more informal discussion of the classical concept of item.