When setting up a passive neutron coincidence counter it is natural to ask what coincidence gate settings should be used to optimize the counting precision. If the gate width is too short then signal is lost and the precision is compromised because in a given period only a few coincidence events will be observed. On the other hand if the gate is too large the signal will be maximized but it will also be compromised by the high level of random pile-up or Accidental coincidence events which must be subtracted. In the case of shift register electronics connected to an assay chamber with an exponential dieaway profile operating in the regime where the Accidentals rate dominates the Reals coincidence rate but where dead-time is not a concern, simple arguments allow one to show that the relative precision on the net Reals rate is minimized when the coincidence gate is set to about 1.2 times the lie dieaway time of the system. In this work we show that making the same assumptions it is easy to show that the relative precision on the Triples rates is also at a minimum when the relative precision of the Doubles (or Reals) is at a minimum. Although the analysis is straightforward to our knowledge such a discussion has not been documented in the literature before. Actual measurement systems do not always behave in the ideal we choose to model them. Fortunately however the variation in the relative precision as a function of gate width is rather flat for traditional safeguards counters and so the performance is somewhat forgiving of the exact choice. The derivation further serves to delineate the important parameters which determine the relative counting precision of the Doubles and Triples rates under the regime considered. To illustrate the similarities and differences we consider the relative standard deviation that might be anticipated for a passive correlation count of an axial section of a spent nuclear fuel assembly under practically achievable conditions.