For the maximum likelihood estimator (MLE) to be unique, the parameter must be both identifiable and estimable. A parameter is identifiable if there is a one-to-one correspondence between parameter values and density functions. A parameter is estimable if the likelihood function has a unique mode. The method of data cloning has been proposed as a way to diagnose structural deficiencies-such as non-identifiability and inestimability-in a model. In this paper, we discuss cases in which this might be problematic, including cases where the number of clones required to detect model deficiencies may be impractically large. We then provide guidelines for more sound identifiability diagnostics.