A simulation study shows that in the presented models, the parameters admit numerically stable estimates as solutions to the maximum likelihood estimating equations. These models have advantage in gauging the examinee’s ability level compared with existing logistic models, since the new models are more flexible and can take into account not only guessing, but cheating phenomenon as well. We illustrate the presented new parameter logistic models with a difficulty-balanced test and conclude that balanced test is preferable compared with usual random sampling approach for testing.