Spatial independent component analysis (sICA) can be applied to human brain functional magnetic resonance imaging (fMRI) data. Here, we address the problem of identifying the "meaningful" subset in the large set of components (ICs). While this problem ultimately requires interpretation, we propose kurtosis of the component histogram, spatial clustering of the component's layout in the brain and one-lag autocorrelation of the time course as criteria useful in selecting components for more in-depth examination. Using our method of cortex-based sICA, we illustrate this selection approach by applying it to two fMRI data sets already well understood by us. The criteria in combination allow the selection of the task-related fMRI-ICs, independent of a priori information pertaining to the particular temporal structure of the experiment.