A Bayesian fitting algorithm was combined with an analytical solution of the Bloch-McConnell equations for multiple CEST pools. The performance of the suggested fitting approach was evaluated in simulated and phantom experiments. Specifically, the application to Taurine-Creatine solutions which exhibit overlapping resonance peaks in the Z-spectrum was investigated. Although the analytical solution introduced biases into the estimated parameters, the estimated exchange rates correlated with the pH of the solutions. Hence, this approach can be applied to detect pH differences based on exchange rate estimates in the case of overlapping resonance peaks in the Z-spectrum.