Many methods are available to tune proportional integral (PI) controllers for first order plus time delay (FOPTD) models of overdamped processes. The two asymptotes for small and large ratios of time delays over time constants are easily calculated. These two asymptotes can be used to evaluate and provide guidelines for the performance and application ranges of PI controller tuning rules. By matching these two asymptotes, a simple analytic tuning rule is suggested. For some overdamped processes whose transfer functions have large zero terms, half-order plus time delay (HOPTD) models are found to yield better results than the FOPTD models. Applying the technique of matching two asymptotes, a simple analytic PI controller tuning rule has also been proposed for the HOPTD models. To apply these tuning rules to high order processes with known transfer functions, model reduction methods to obtain the FOPTD and HOPTD models are investigated. Simulation results for empirical and full models of processes show the performances of the proposed model reduction methods and tuning rules.