Genome-wide association studies (GWAS) search for associations between genetic variants and disease status, typically via logistic regression. Often there are covariates, such as sex or well-established major genetic factors, that are known to affect disease susceptibility and are independent of tested genotypes at the population level. We show theoretically and with data from recent GWAS on multiple sclerosis, psoriasis and ankylosing spondylitis that inclusion of known covariates can substantially reduce power for the identification of associated variants when the disease prevalence is lower than a few percent. Whether the inclusion of such covariates reduces or increases power to detect genetic effects depends on various factors, including the prevalence of the disease studied. When the disease is common (prevalence of >20%), the inclusion of covariates typically increases power, whereas, for rarer diseases, it can often decrease power to detect new genetic associations.