Bifactor structures generally fit better to the data than simple first order models. However, when the latent structure is unknown, deciding the number of specific factors is not a trivial task. A strategy involves comparing the fit of several bifactors using ESEM, though it is only possible in a few software. The goal of the present research is to propose a method to explore the bifactor structures using parallel analysis (PA) of the residuals of one-dimensional models, in order to decide how to retain specific factors. The benefit of the PA is related with the its wide implementation in manifold software. The method consists in two steps: First, set up a unidimensional model, and save the residual covariance matrix; second, perform a PA on the residual matrix. We simulate five datasets, aiming to evaluate this method, setting the following ‘true models’: Unidimensional, bifactors with high loadings on a general factor, and bifactors with low loadings on a general factor. We also set bifactors with three and four specific factors. The datasets, composed by 1.000 subjects each, were simulated trough Montecarlo. The results of the PA of the residual covariance indicated the retention of the number of the true factors minus one (considering all the datasets based on a bifactor true structure). Although this result was not expected, it can be explained: In the first step, the unique dimensional tend to explain the great part of the variance of the items which compose the first specific dimension. Then, the residual contains only the items covariance of the second and forwards specific dimensions. The residual PA of the unidimensional dataset yielded a non-positive matrix, as expected. Future researches might test the PA in models setting high loadings on a general factor only for those items starting from the second specific factors.