The goal of multiple group factor analysis is to study measurement invariance and also group differences in factor means and variances. This is typically carried out using confirmatory factor analysis with equality constraints. A radically different method is proposed which is particularly useful when there are many groups with many non-invariant parameters as is common in cross-cultural studies. The method has three steps. Step is a configural factor analysis with no across-group restrictions. Step 2 makes a rotation according to a simplicity criterion that favors few non-invariant measurement parameters. Step 3 adjusts the factor means and factor variances in line with the rotation. Applications include cross-cultural data from the ESS.