The concept of construct-focused configural invariance is proposed for investigating the measurement invariance of measures that need to be represented by means of a multi-dimensional model with constrained discriminability. The major characteristic of this concept is the concentration of the investigation of invariance on the component representing the process or processes associated with the construct of interest. This concept enables the exclusion of other components accounting for irrelevant but systematic variance from an investigation. Three large sets of Exchange Test data that differed according to the applied version of the Exchange Test and the population from which the samples originated were investigated according to this concept. Two samples were university students and the third one internet users. It was possible to establish construct-focused configural invariance and corresponding metric invariance for Exchange Test.