Motivated by applications in biostatistics, I will discuss computational methods for various constrained generalized linear models (GLMs) in which the linear predictor cannot range over the entire real line. Common examples include the binomial model with log or identity link, and the Poisson model with identity link. These models are important in biostatistics for obtaining adjusted relative risks, risk differences and rate differences. I will begin by illustrating the surprisingly unstable iterative behavior exhibited by conventional GLM software (primarily using R). This instability stems from the fact that Fisher scoring may have a repelling fixed point for such non-canonical models, which can induce periodicity and chaos in the iterative sequence. I will then discuss a class of algorithms called combinatorial EM (CEM) algorithms, which are an extension of the standard EM algorithm. CEM algorithms provide a stable alternative to standard GLM algorithms and are particularly suited to semi-parametric extensions through generalized additive models. I will primarily use the log link binomial model as a case study, including some practical data analysis examples, but I will also mention how CEM algorithms apply to other models.