The identification of a class of ill-conditioned processes is considered. The goal of identification is model predictive control (MPC). For this class of processes, it is essential to have good estimation of the very small difference between certain transfer functions, or, low gain direction. Two simple and practical test methods will be proposed that can enhance the model quality of low gain direction. The main idea is to use the high amplitude and high correlation test signals that excite the low gain direction more and that will not disturb process operation. The test signals can be used in both open-loop and closed-loop tests. A high purity distillation column model is used to show the effectiveness of the methods.