In this paper, a 3D surface scanner is presented. Combining stereovision and slit-scanning, our system is composed of two cameras and a hand-held laser plane. The camera pair is calibrated using synchronized image pairs of a coded chessboard; its imaged nodes are automatically identified, referred to the object points and introduced into a self-calibrating bundle adjustment. For the scanning process, stereoscopic profiles are continuously recorded as the 3D surface is swept by the laser line. After epipolar resampling of the synchronized image pairs, search for point correspondences is thus reduced to identifying intersections of image rows with the re-corded laser profiles. The maxima of Gaussian curves fitted to the gray-value data along the epipolar image rows provide initial esti-mates for peak positions, which are then refined using information from their neighbourhood. In our setup, 3D reconstruction by simple stereovision is strengthened by enforcing extra geometric constraints. First, the coplanarity constraint is imposed on all 3D points reconstructed from a single laser stripe, and the coefficients of all laser planes participate as unknowns in the 3D recon-struction adjustment. Additionally, this also allows identifying mismatches since epipolar lines may have more than one peaks; the correct 3D point is established according to a distance threshold from the laser plane. The solution is further reinforced by placing the object in a corner formed by two background planes (which are scanned along with the object), whose coefficients are also unknowns in the 3D reconstruction adjustment. The linear laser segments produced on either side of the object have to satisfy the equation of both the corresponding plane and the laser plane. Image pairs of the corner without the object (longer laser segments) are added to the dataset for a more accurate determination of plane equations. Results are presented and evaluated from this setup, whose typical accuracy is estimated in the order of 0.2 mm in 3D depth estimation.