Research on computer-supported collaborative learning (CSCL) has strongly emphasized the value of providing student support with micro-scripts, which should withdraw (fade-out) allowing students to practice the acquired skills. However, research on fading shows conflicting results and some researchers suggest that the impact of fading is enhanced when the peer-monitoring technique is additionally implemented. This study investigates the effectiveness of micro-script fading in computer-supported argumentation activity in contrast to the peer-monitoring technique, as a means to enhance students' learning outcomes. Thirty four (34) students collaborated remotely in dyads (in lab conditions) on a task guided by a micro-script for argumentation. The dyads were divided in (a) the control group (with continuous script support); (b) the fading group (with the script fading-out after some student posts), and (c) the peer-monitoring group (with continuous script support and with prompts that students monitor their peer contributions). Students in the peer-monitoring group outperformed those in both the control group and the fading group in domain-specific knowledge acquisition post-test items. Overall, this study provides evidence that enriching argumentation scripts with the peer-monitoring technique can substantially improve learning outcomes, while simply fading-out the micro-script does not seem to improve student learning in any aspect. (Contains 8 tables and 4 figures.)