When drawing real scenes or copying simple geometric figures young children are highly sensitive to parallel cues and use them effectively. However, this sensitivity can break down in surprisingly simple tasks such as copying a single line where robust directional errors occur despite the presence of parallel cues. Before we can conclude that this directional bias is a limiting case it needs to be shown that any given parallel cues are indeed being processed. We achieved this by using a texture-defined contour where parallel cues are integral to the stimulus and thus cannot be ignored. Here we report that even when prolific parallel cues must have been processed, young children make robust directional errors when copying single lines. This finding demonstrates a major constraint on young children's spatial parallel coding.