Collaboration scripts and heuristic worked examples have been described as powerful scaffolds to support skill acquisition in CSCL. While CSCL scripts particularly facilitate argumentative discourse within groups, heuristic worked examples provide heuristics and worked out pathways to solve domain-specific tasks. Yet, both scripts and heuristic worked examples are often designed in a one-size-fits-all fashion. Granting learners the opportunity to adapt these scaffolds to their self-perceived needs might be a way to further enhance their effects. We tested this assumption in two experiments. In experiment 1, we compared the effects of learning with adaptable and non-adaptable CSCL scripts. In experiment 2, we compared the effects of learning with adaptable and non-adaptable heuristic worked examples. University students (N = 167) learned repeatedly in pairs with either adaptable or non-adaptable scaffolding in the context of mathematical conjecture problems. Results show that adaptable CSCL scripts were partly helpful for students with higher levels of self-regulation skills. Non-adaptable maximal scaffolding supported learning of distinctive skill components. Social-discursive components were best facilitated by maximal heuristic worked examples through content knowledge scaffolds. In contrast, CSCL scripts best facilitated domain-specific skill components by scaffolding learners' engagement in social discourse about domain knowledge. The study provides recommendations for designing adaptable scaffolding by taking into account the relation between the targeted skill component and the activities scaffolded in the learning process. We suggest conducting future studies on adaptable scaffolding with a focus on supporting learning regulation and group awareness to improve learners' success in CSCL environments.