Genetic improvement of categorically recorded traits is hampered because information content of categorical records is low and ordinary linear breeding value estimation methods do not apply theoretically. The ordinary animal or linear mixed model (LMM), which ignored the categorical nature of the trait, is compared to a generalized linear mixed model (GLMMp) that assumes a linear mixed model for an underlying continuous variable. The GLMMp takes full account of the categorical nature of the trait and is a straightforward extension of LMM. In a closed nucleus breeding scheme (e.g., cattle, pigs, or poultry), rates of genetic gain increased by 1 to 2%, when GLMMp was used instead of LMM. Rates of genetic gain increased by 7 to 20%, when the best sires were used on the best herds (i.e., when there was some confounding between sire and herd effects). When considering a binary trait (e.g., disease incidence) initial incidences of 25% could be reduced to 2.8% within 10 generations of selection. Rates of gain can be increased by up to 84% by gathering more information on high-incidence categories (i.e., by dividing these categories into subcategories). Subdividing low-incidence categories (e.g., splitting diseased animals into moderately and severely diseased) hardly increased rates of gain. Direct recording of the underlying variable, which requires uncovering of the physiological background of the categorical trait, yielded 109 to 278% more genetic gain than selection for a binary trait.