Heart rate variation due to respiration is a window onto autonomic nervous system function and many measures exist that quantify this variability. Computer-based simulations of 1-minute deep-breathing tests, along with common artifacts, were used to compare the most frequently used measures. We found distinct differences in the performance of the measures. Some measures (e.g., SDRR and MSSD) are strongly influenced by the underlying mean heart rate while others (e.g., Max-Min and SDHR) are not. All of the measures tested, except R, were influenced by both shifting mean heart rate and single-beat anomalies. R, on the other hand, is strongly influenced by test duration and breathing asynchronies. Sensitivity to phenomena unrelated to ANS function can reduce the diagnostic discrimination of these measures. We suggest simple improvements to the measures and discuss how some measures may be theoretically superior to others.