bash process substitutions:
command_a 2> >(sed 's/^/command_a: /' >&2) > command_a.log & command_b 2> >(sed 's/^/command_b: /' >&2) > command_b.log & You don't need to pipe to tee if you just redirect it's stdout to a file.
You can even do fancy stuff like print a timestamp:
$ { date echo stdout sleep 3 echo stderr >&2 } 2> >(gawk '' >&2) > file.log foobar: [2015-02-24 11:43:32] stderr $ cat file.log Tue Feb 24 11:43:29 EST 2015 stdout Stick it in a function for re-use:
log_stderr() { gawk -v pref="$1" '' >&2 } command_a > command_a.log 2> >(log_stderr "command_a")