Global voting schemes based on the Hough transform (HT) have been widely used to robustly detect lines in images. However, since the votes do not take line connectivity into account, these methods do not deal well with cluttered images. On the other hand, the so-called local methods enforce connectivity but lack robustness to deal with challenging situations that occur in many realistic scenarios, e.g., when line segments cross or when long segments are corrupted. We address the critical limitations of the HT as a line segment extractor by incorporating connectivity in the voting process. This is done by only accounting for the contributions of edge points lying in increasingly larger neighborhoods and whose position and directional information agree with potential line segments. As a result, our method, which we call segment extraction by connectivity-enforcing HT (STRAIGHT), extracts the longest connected segments in each location of the image, thus also integrating into the HT voting process the usually separate step of individual segment extraction. The usage of the Hough space mapping and a corresponding hierarchical implementation make our approach computationally feasible. We present experiments that illustrate, with synthetic and real images, how STRAIGHT succeeds in extracting complete segments in situations where current methods fail.