Shared Virtual Environments (SVEs) have been extensively researched for education, entertainment, work, and training, yet there has been limited research on the creative aspects of collaboration in SVEs. This raises questions about how to design virtual working spaces to support collaborative creativity in SVEs. In this paper, we outline an SVE named LeMo, which allows two people to create music collaboratively. Then we present a study of LeMo, in which 42 users composed music together using three different virtual working space configurations. Results indicate that (i) two types of territory and working configurations emerged during collaborative composing (ii) when made available to them, personal working spaces were extensively used, and were considered to be essential to successful collaborative music making and (iii) a publicly visible personal working space was preferable to a publicly invisible one. Based on these findings, three corresponding design implications for Shared Virtual Environments focusing on supporting collaborative creativity are given.