The problem in the unparented (left) results, which I didn't notice, was that the internal names use two different suffix sequences. That's the answer I just found - it's down to whether there's an underscore in the 'prop'field of the PP2.

The first problem in the parented (right) results, which I also overlooked, was the :1 and :2 suffixes.I found the answer to that on the previous page - they appear for parented props, with the value being the same as the :# suffix for every actor in the parent.

The second problem in the parented (right) results is the fact that the EXTERNAL name for IcyingLight uses a different suffix sequence from the other two props. This was the original problem for which I started this thread.

It now seems to me that the best approach is to start with the IcyingLight PP2 and change it bit by bit until it's the same as one of the others.At some point the suffixes should change,and I should have the answer.

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The 3Dcheapskate (also available in DAZ and HiveWire3D flavours) occasionally posts sensible stuff. Usually by accident.
And it usually uses Poser 11, with units set to inches. Except when it's using Poser 6 or PP2014, or when its units are set to PNU.