Pseudomonas aeruginosa quorum sensing (QS) regulates expression of dozens of genes in a cell density-dependent manner. Many QS-regulated genes code for production of extracellular factors, "public goods" that can benefit the entire population. This cooperation encourages individuals to cheat by using but not producing public goods. QS also controls expression of a limited number of genes encoding "private" cellular enzymes like Nuh, an enzyme involved in adenosine catabolism. Growth of P. aeruginosa on casein requires QS-regulated production of an extracellular protease and is an example of cooperative behavior. When P. aeruginosa is transferred daily on casein, QS mutants emerge. These cheaters have mutations in lasR, which encodes the primary QS transcription factor. When growth is on casein and adenosine, cheater emergence is constrained. Here, we report the dynamics of LasR mutant invasion during growth on casein or casein plus adenosine. We show that LasR mutants have the greatest advantage during early to mid-logarithmic growth on casein. Addition of adenosine to casein medium constrains cheaters throughout growth. Our data support the view that co-regulation of the public protease and the private nucleosidase by QS stabilizes cooperation, and the data are not consistent with other proposed alternate hypotheses.