The apparent length and orientation of short lines is altered when they abut against oblique lines (the Zöllner and Judd illusions). Here we present evidence that the length and orientation biases are geometrically related and probably depend upon the same underlying mechanism. Measurements were done with an 'H' figure, in which the apparent length and orientation of the cross-bar was assessed by the method of adjustment while the orientation of the outer flanking lines was varied. When the flanking lines are oblique the apparent length of the central line is reduced and its orientation is shifted so that it appears more nearly at right-angles to the obliques than is in fact the case. Measurements of the orientation and length effects were made in three observers, over a range of flanking-line angles (90, 63, 45, 34 and 27 deg) and central line lengths (9, 17, 33 and 67 arc min). The biases increased with the tilt of the flanking-lines, and decreased with central line length. The extent of the length bias could be accurately predicted from the angular shift by simple trigonometry. We describe physiological and computational models to account for the relation between the orientation and length biases.