The celebrated Calderon-Zygmund Lemma plays a key role in the real variable analysis of singular integrals. However, as the coefficients of the differential equations or the underline domains become less smooth, the operators involved are not necessarily bounded on every L^p spaces. In this talk I will describe a new variable method which may be regarded as a refined version of the Calderon-Zygmund Lemma. We will illustrate it s applications in the study of boundary value problems in non-smooth domains and of boundedness of Riesz transforms associated to general second order elliptic operators.