It must be remembered that, particularly for complex multicomponent models, the chi-squared surface may have local minima. The program will generally settle down into the closest such minimum, so it is important to start from a reasonable point in parameter space. With complex models it is often helpful to start by fitting a subset of the model to get some parameters into the right regime. e.g. where a line is present, it is best to fit the underlying continuum first, before adding the line to the model. It may also improve stability to freeze line width at a small value until position and strength have been optimised.
Some of the more complex models (e.g. ST and CS) are valid only within a limited volume of parameter space which may have complex boundaries (depending on combinations of parameter values). If the bounds of the region of validity are transgressed during the fitting process then the user will be warned (each time!). If the FINAL fit values are outside the valid region then the result is suspect, otherwise no harm has been done.