Spatially focal source estimates for magnetoencephalography (MEG) and electroencephalography (EEG) data can be obtained by imposing a minimum ℓ1-norm constraint on the distribution of the source currents. Anatomical information about the expected locations and orientations of the sources can be included in the source models. In particular, the sources can be assumed to be oriented perpendicular to the cortical surface. We introduce a minimum ℓ1-norm estimation source modeling approach with loose orientation constraints (ℓ1LOC), which integrates the estimation of the orientation, location, and strength of the source currents into a cost function to jointly model the residual error and the ℓ1-norm of the source estimates. Evaluation with simulated MEG data indicated that the ℓ1LOC method can provide low spatial dispersion, high localization accuracy, and high source detection rates. Application to somatosensory and auditory MEG data resulted in physiologically reasonable source distributions. The proposed ℓ1LOC method appears useful for incorporating anatomical information about the source orientations into sparse source estimation of MEG data. Hum Brain Mapp 34:2190–2201, 2013. © 2011 Wiley Periodicals, Inc.