tar stops with "Cannot stat: No such file or directory"

tar complains about not finding a directory that exists, and to which I have permissions. I have seen a number of similar questions, but all of them had to do wih the option f not being just before the output file. Not the case here.

gauthier@ionian:~ $ ls -l | grep cpdata
drwxrwxr-x   2 gauthier gauthier     4096 May 23 14:35 cpdata
-rw-rw-r--   1 gauthier gauthier 17609833 May 23 14:43 cpdata.tar.gz
gauthier@ionian:~ $ echo $HOME
/home/gauthier
gauthier@ionian:~ $ sudo tar -cvzf ~/cpd.tar.gz ~/cpdata
tar: Removing leading `/' from member names
tar: /home/gauthier/cpdata: Cannot stat: No such file or directory
tar: Exiting with failure status due to previous errors
gauthier@ionian:~ $ tar --version
tar (GNU tar) 1.27.1
Copyright (C) 2013 Free Software Foundation, Inc.
License GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>.
This is free software: you are free to change and redistribute it.
There is NO WARRANTY, to the extent permitted by law.

Written by John Gilmore and Jay Fenlason.
gauthier@ionian:~ $ pwd
/home/gauthier

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