Boosting techniques present a popular alternative to conventional methods for estimating covariate effects in generalized linear mixed models. Additionally to functionality in high-dimensional data setups, they also offer variable selection. The established framework for boosting in GLMMs tends to exhibit problematic behavior in the selection process when cluster-constant covariates are present, which leads to incorrect estimates. We propose an improved algorithm that rectifies this issue by reworking the updating process of the random effects which already proved successful for linear mixed models, i.e. normally distributed outcomes, and provide additional insights regarding the computation of model complexity. We show the improvements in the quality of estimates via various simulations and data examples.