Independent component analysis (ICA) is a data-driven approach utilizing high-order statistical moments to find maximally independent sources that has found fruitful application in functional magnetic resonance imaging (fMRI). Being a blind source separation technique, ICA does not require any explicit constraints upon the fMRI time courses. However, for some fMRI data analysis applications, such as for the analysis of an event-related paradigm, it would be useful to flexibly incorporate paradigm information into the ICA analysis. In this paper, we present an approach for constrained or semi-blind ICA (sbICA) analysis of event-related fMRI data by imposing regularization on certain estimated time courses using the paradigm information. We demonstrate the performance of our approach using both simulations and fMRI data from a three-stimulus auditory oddball paradigm. Simulation results suggest that (1) a regression approach slightly outperforms ICA when prior information is accurate and ICA outperforms the general linear model (GLM)-based approach when prior information is not completely accurate, (2) prior information improves the robustness of ICA in the presence of noise, and (3) ICA analysis using prior information with temporal constraints can outperform a regression approach when the prior information is not completely accurate. Using fMRI data, we compare a regression-based conjunction analysis of target and novel stimuli, both of which elicit an orienting response, to an sbICA approach utilizing both the target and novel stimuli to constrain the ICA time courses. Results show similar positive associations for both GLM and sbICA, but sbICA detects additional negative associates consistent with regions implicated in a default mode of brain activity. This suggests that task-related default mode decreases have a more "complex" signal that benefits from a flexible modeling approach. Compared with a traditional GLM approach, the sbICA approach provides a flexible way to analyze fMRI data that reduces the assumptions placed upon the hemodynamic response of the brain. The advantages and limitations of our technique are discussed in detail in the manuscript to provide guidelines to the reader for developing useful applications. The use of prior time course information in a spatial ICA analysis, which combines elements of both a regression approach and a blind ICA approach, may prove to be a useful tool for fMRI analysis.