To cope with the severe masking of background cerebral activity in the electroencephalogram (EEG) by ocular movement artefacts, we present a method which combines lower-order, short-term and higher-order, long-term statistics. The joint smoothened subspace estimator (JSSE) calculates the joint information in both statistical models, subject to the constraint that the resulting estimated source should be sufficiently smooth in the time domain (i.e., has a large autocorrelation or self predictive power). It is shown that the JSSE is able to estimate a component from simulated data that is superior with respect to methodological artefact suppression to those of FastICA, SOBI, pSVD, or JADE/COM1 algorithms used for blind source separation (BSS). Interference and distortion suppression are of comparable order when compared with the above-mentioned methods. Results on patient data demonstrate that the method is able to suppress blinking and saccade artefacts in a fully automated way.