The paper presents a method for model updating, called Quadratic Compression Method (QCM). The updated model has a fixed structure with some free parameters. Algebraic manipulations of the eigenvalue equation lead to a simplified equation with a lower dimension. This equation is then solved in a Least Squares sense. The method is shown to belong to the class of Minimization of the Error in the Characteristic Equation (MECE), with a particular choice of the weighting matrix. The paper presents also a weighted version of the method, called WQCM, which is motivated by reducing the effect of measuring noise. In addition to the theoretic analysis, the superior robustness to noise properties of QCM and WQCM are demonstrated by simulations and experimentally.