An example of balanced data with small sample size is used to illustrate difficulties in analyses with mixed models including those using the Kenward and Roger (KR) method. The data contains 8 sites, each with two treatment groups, 20 animals per site (10 animals per treatment group), zero covariance for site, and nonzero covariance for the interaction of ‘Treatment by Site’. The outcome of interest is binary (success/failure). ‘Treatment’ is a fixed effect, while ‘Site’ and the interaction ‘Treatment by Site’ are random effects. The full and constrained models are investigated using SAS PROC GLIMMIX with and without the KR option and with and without the ‘nobound’ option. Results are compared.