In confirmatory factor analysis (CFA), model parameters are usually estimated by iteratively minimizing the Maximum Likelihood (ML) fit function. In optimal circumstances, the ML estimator yields the desirable statistical properties of asymptotic unbiasedness, efficiency, normality, and consistency. In practice, however, real-life data tend to be far from optimal, making the algorithm prone to convergence failure, inadmissible solutions, and bias. In this study, we revisited some old, yet largely neglected non-iterative alternatives and compared their performance to more recently proposed procedures in an extensive simulation study. We conclude that closed-form expressions may serve as viable alternatives for ML, with the Multiple Group Method -- the oldest method under consideration -- showing favorable results across all settings.