FastICA is arguably one of the most widespread methods for independent component analysis. We focus on its deflation-based implementation, where the independent components are extracted one after another. The present contribution evaluates the method’s speed in terms of the overall computational complexity required to reach a given source extraction performance. FastICA is compared with a simple modification referred to as RobustICA, which merely consists of performing exact line search optimization of the kurtosis-based contrast function. Numerical results illustrate the speed limitations of FastICA.