A method for embedding ultraviolet (UV) responsive watermarks in CMY printed halftone images, named white modulation (WM), was proposed recently, which is based on the iterative color direct binary search (CDBS) halftoning framework. The CDBS-WM method embeds a visual watermark by modulating the local white paper coverage in order to create a differential response under UV illumination through the substrate fluorescence. In this paper, we present two main extensions of CDBS-WM. First, we propose a printer model suitable for UV watermark embedding in multi-channel printer scenarios-using four or more inks. Second, we propose an improved cost function that is minimized during the CDBSbased iterative embedding that takes into account the UV response of all primaries, as opposed to only the white primary in CDBS-WM. The proposed extensions increase the perceptual uniformity of the embedded UV watermark, as well as the UV watermark strength especially in certain image areas where the CDBS-WM failed to embed watermark.