A method for testing optical fibers includes using an optical testing instrument to measure a characteristic, such as clad non-circularity, of an optical fiber at a multiple angles of rotation of an optical fiber around its optical axis. From the measurements data points indicative of measured values of the characteristic at the respective angles of rotation are generated. A model is created of the optical fiber having the characteristic as a variable parameter, and from the model a functional relationship between an expected measured value of the characteristic and the angle of rotation and the variable parameter is generated. By varying the parameter a fit of the functional relationship to the data points is made according to one or more predetermined criteria, such as least-squares fit. The value of the characteristic can be found based on the fit. Instrumental parameters, such as fiber misalignment and cleave angle, can also be ascertained by the method.