Thyroid nodules are solid or cystic lumps formed in the thyroid gland and may be caused by a variety of thyroid disorders. This paper presents a novel active contour model for precise delineation of thyroid nodules of various shapes according to their echogenicity and texture, as displayed in ultrasound (US) images. The proposed model, named joint echogenicity-texture (JET), is based on a modified Mumford-Shah functional that, in addition to regional image intensity, incorporates statistical texture information encoded by feature distributions. The distributions are aggregated within the functional through new log-likelihood goodness-of-fit terms. The JET model requires only a rough region of interest within the thyroid gland as input and automatically proceeds with precise delineation of the nodules, revealing their shape and size. The performance of the JET model was validated on a range of US images displaying hypoechoic and isoechoic nodules of various shapes. The quantification of the results shows that the JET model: 1) provides precise delineations of thyroid nodules as compared to "ground truth" delineations obtained by experts and 2) copes with the limitations of the previous thyroid US delineation approaches as it is capable of delineating thyroid nodules regardless of their echogenicity or shape.