This research brief presents a selection of findings from a four-year, mixed-methods study of a cohort of new entrants to the child care subsidy programs in four selected sites in Illinois and New York. The broader study includes an analysis of data from a telephone survey with subsidy clients, in-depth interviews with a subset of survey respondents, and state administrative records that track subsidy participation over an 18-month period. This brief reports findings from the in-depth interviews to the following questions: What do clients recommend to improve the subsidy program to better support families? Are there subsidy program characteristics and job characteristics that parents perceive as hindering subsidy stability and child care continuity? We conclude with a discussion of how these findings align with subsidy policies in the Child Care and Development Block Grant (CCDBG) Act of 2014. (author abstract)