Friction dampers have been used to reduce turbine blade vibration levels for a considerable period of time. However optimal design of these dampers has been quite difficult due both to a lack of adequate theoretical predictions and to difficulties in conducting reliable experiments. One of the difficulties of damper weight optimization via the experimental route has been the inevitable effects of mistuning. Also, conducting separate experiments for different damper weights involves excessive cost. Therefore, current practice in the turbomachinery industry has been to Conduct so-called "rainbow tests" where friction dampers with different weights are placed between blades with a predefined configuration. However, it has been observed that some rainbow test results have been difficult to interpret and have been inconclusive for determining the optimum damper weight for a given bladed-disk assembly. A new method of analysis-a combination of the harmonic balance method and structural modification approaches-is presented in this paper for the analysis of structures with friction interfaces and the method is applied to search for qualitative answers about the so-called "rainbow tests" in turbomachinery applications. A simple lumped-parameter model of a bladed-disk model was used and different damper weights were modeled using friction elements with different characteristics. Resonance response levels were obtained for bladed disks with various numbers of blades under various engine-order excitations. It was found that rainbow tests, where friction dampers with different weights are used on the same bladed-disk assembly, can be used to find the optimum damper weight if the mode of vibration concerned has weak blade-to-blade coupling (the case where the disk is almost rigid and blades vibrate almost independently from each other). Otherwise, it is very difficult to draw any reliable conclusion from such expensive experiments.