I show analytically that compensation for thermal blooming by full-field conjugation with perfect phase reproduction but with a saturable laser amplifier exhibits instability, which leads to strong scintillation on small spatial scales. I support this analysis with output from MOLLY, a computer simulation of adaptively compensated high-energy laser-beam propagation. In the simulation, compensation for thermal blooming is effective in spite of manifest instability. I derive lower bounds on compensation performance that highlight aspects of the simulation that are responsible for good performance.