Malignant skin lesions are among the most common types of cancer, and automated systems for their early detection are of fundamental importance. We propose SDI+, an unsupervised algorithm for the segmentation of skin lesions in dermoscopic images. It is articulated into three steps, aimed at extracting preliminary information on possible confounding factors, accurately segmenting the lesion, and post-processing the result. The overall method achieves high accuracy on dark skin lesions and can handle several cases where confounding factors could inhibit a clear understanding by a human operator. We present extensive experimental results and comparisons achieved by the SDI+ algorithm on the ISIC 2017 dataset, highlighting the advantages and disadvantages.