This paper proposes an advanced method for contrast enhancement of capsule endoscopic images, with the main objective to obtain sufficient information about the vessels and structures in more distant (or darker) parts of capsule endoscopic images. The proposed method (PM) combines two algorithms for the enhancement of darker and brighter areas of capsule endoscopic images, respectively. The half-unit weighted bilinear algorithm (HWB) proposed in our previous work is used to enhance darker areas according to the darker map content of its HSV's component V. Enhancement of brighter areas is achieved thanks to the novel thresholded weighted-bilinear algorithm (TWB) developed to avoid overexposure and enlargement of specular highlight spots while preserving the hue, in such areas. The TWB performs enhancement operations following a gradual increment of the brightness of the brighter map content of its HSV's component V. In other words, the TWB decreases its averaged-weights as the intensity content of the component V increases. Extensive experimental demonstrations were conducted, and based on evaluation of the reference and PM enhanced images, a gastroenterologist ({\O}H) concluded that the PM enhanced images were the best ones based on the information about the vessels, contrast in the images, and the view or visibility of the structures in more distant parts of the capsule endoscopy images.