[Context and Motivation] Modern society is facing important challenges that are critical to improve its environmental performance. The literature reports on many green strategies aimed at reducing energy consumption. However, little research has been carried out so far on including green strategies in software design. [Question/problem] In this paper, we investigate how green software strategies can contribute to, and influence, quality requirements prioritization performed iteratively throughout a service-oriented software design process. [Methodology] In collaboration with a Dutch industry partner, an empirical study was carried out with 19 student teams playing the role of software designers, who completed the design of a real-life project through 7 weekly deliverables. [Principle ideas/results] We identified a list of quality requirements (QRs) that were considered by the teams as part of their architectural decisions when green strategies were introduced. By analyzing relations between QRs and green strategies, our study confirms usability as the most used QR for addressing green strategies that allow to create people awareness. Qualities like reliability, performance, interoperability, scalability and availability emerged as the most relevant for addressing service-awareness green strategies. [Contribution] If used at the beginning of a green software project, our results help including the most relevant QRs for addressing those green software strategies that are e.g. the most domain-generic (like increase carbon footprint awareness, paperless service provisioning, virtualization).