"gzip: stdin has more than one entry--rest ignored" and "gzip: tmp.gz has more than one entry -- unchanged"
Solution 1:
As explained by 'druuna' at http://www.linuxquestions.org/questions/linux-software-2/gunzip-%5Bfile%5D-has-more-than-one-entry-unchanged-618990/#post3047709, this can happen if it's actually a ZIP-file rather than a gz-file, just with a misleading extension, and it contains multiple files. (gzip -d does support ZIP-files that contain only one file.)
In my case, that's exactly right:
$ file tmp.gz
tmp.gz: Zip archive data, at least v2.0 to extract
and using unzip rather than gzip -d worked perfectly.