Summary: Most users of Structural Equation Models are aware that Wald-type standard errors for parameter estimates can vary remarkably depending on the arbitrary choice of how the scale is identified. When the focus is on $Ho$: coefficient is 0, tests based on a likelihood-ratio are invariant to the scale identification. However, a simple example shows that confidence intervals based on the likelihood ratio exhibit the same problem. A series of examples suggests that shopping for the scale identification that gives the best relative precision for a certain parameter has very little negative impact on coverage probabilities, and can yield substantially tighter confidence intervals.