Context: Several software changes applied while evolving software features aim at improving internal quality attributes, e.g. cohesion. These changes are the refactorings. Non-assisted refactorings might worsen, rather than improve, internal attributes. However, current knowledge is insufficient for managing internal attributes during software evolution. Objective: Our first objective is assessing how refactorings affect internal attributes during software evolution by filling gaps of past work on study scope. Our second objective is filling gaps of qualitative evidence on how to manage critical internal attributes via refactorings while evolving features. An internal attribute is critical when its measurement has anomalous values. Low cohesion is an example of critical attribute. Method: Our first study extends a large quantitative assessment of the relationship between refactorings and five internal attributes: cohesion, complexity, coupling, inheritance, and size. We include a more detailed statistical analysis and address major threats to validity of past work. Our second study is a qualitative case study based on focus group. We selected two industry cases to promote discussions on how much (and why) critical attributes are relevant while evolving features. Finally, we crossed the findings from both conducted studies aimed at discussing how critical attributes can be addressed via refactoring when evolving features. Results: About 64 per cent of refactorings either improve or keep the internal attributes unaffected. Developers seem to perform refactorings until the most relevant internal attributes are improved, thereby neglecting other internal attributes that may be critical. Low cohesion and high complexity are perceived as relevant because they often make evolving features harder than usual. High coupling, large inheritance, and large size are perceived as irrelevant when developers implement especially complex features. By crossing the findings from both studies, we discuss how refactorings can improve internal attributes, especially the critical ones. Conclusions: The findings of our studies can support managing critical attributes that developers typically find relevant, while preserving other attributes that may become critical.