Thanks, Acadia, but I don't think that that's it.   If I keep Poser open, while I check the output in Photoshop, I can go back and save the same picture again.   When I do that, TIFF is already selected, because it is the format which I have previously selected for the original saved file, and this new version is correctly stored .    The second saved file will be identical in size to the original, too, because they really are both TIFFs.   I can correct the first file by changing the extension type.

Poser is storing the right format, but the wrong extension and I don't think that there is anything that I am doing to make that happen, beyond choosing to save a TIFF.

...Incidentally, I never use "Export".   I always use the "Tear-off" icon above the render window.   The functions should be identical, though.