Let \(Y\) be data from a countable data space \(\mathcal Y\) with distribution depending on \((\vartheta,\psi)\), where \(\vartheta\in R\) is a parameter of interest and \(\psi\) is a nuisance parameter. The Bueheler (exact) \(1-\alpha\) upper confidence limit based on a statistics \(T=t(Y)\) is defined as \(u^*(Y)\), where \[ u^*(y)=\sup\{\vartheta:\;\sup_\psi g(\vartheta,y)>\alpha\}, \qquad g(\vartheta,y)=\sup_\psi {\mathbf{P}}\{t(Y)\leq t(y)\;| \;\vartheta,\psi\}. \] The author demonstrates that \(g(\vartheta,y)\) is a nondecreasing function of \(\vartheta\) \(\forall y\in\mathcal Y\) for a wide class of models which satisfy a “logical ordering” condition. This simplifies the procedure of \(u^*(Y)\) computations. A confidence interval for \(\vartheta=\lambda_1-\lambda_2\) by the data \(Y=(Y_1,Y_2)\), \(Y_i\) being independent Binomial\((n_i,\lambda_i)\), is considered as an example. Numerical results and comparison of different statistics \(T\) are presented.