Polyamory is the practice of having multiple emotionally close relationships that may or may not be sexual. Research concerning polyamory has just begun to determine how relationships among partners in polyamorous arrangements may vary. Most of the research assessing perceptions of polyamorous partners has focused on primary-secondary configurations; however, non-hierarchical configurations exist and can involve having multiple primary partners or having only non-primary partners. The current research is the first to examine perceptions of partners and relationship quality in various polyamorous configurations and compares results for each configuration to monogamous partners. Results from online convenience samples suggest that co-primary and non-primary configurations are common among polyamorous participants, with approximately 38% identifying with one of these configurations in 2013 and 55% in 2017. Furthermore, our results suggest that while relationships with partners in co-primary and non-primary structures still differ in some ways (e.g., investment, acceptance, secrecy, time spent having sex), they are closer to their ideals on several psychologically meaningful indicators of relationship quality (e.g., commitment and satisfaction). In other words, despite rejecting hierarchical primary-secondary labels, many of the same relationship qualities differ systematically among partners in non-hierarchical relationships. Furthermore, pseudo-primary partners and primary partners in these relationships are more comparable to monogamous partners than they are to secondary partners. We discuss how these results inform our understanding of polyamorous and monogamous relationships and suggest future directions based on these findings.