Regex to remove subdirectory

I need to remove subdirectories that are empty and I've not done this before. First I am going through the files to remove old records. Then if the directory is empty I want to delete it. There are files in /direcotry/images/fs* - 0-9 and a-z The fs* directories need to stay, but any directories under the fs* directories that are empty need to be removed. Did I explain this ok?
So far I have this:

DIRECTORY=/directory/images
DATESTAMP="`date '+%m%d%y_%H:%M'`"
LOG_DIR=${TRAFFIC_IMAGE_HOME}/log
LOG=${LOG_DIR}/tiffsRemoved.${DATESTAMP}.txt
# this works fine -- 
for file in $( find $DIRECTORY -type f -name '*.tif' -mtime +15 )
do
  echo $file
  rm -rf $file
done | sort >> "$LOG"

# I can't figure out how to do this- 

for dir in $( find $DIRECTORY -type d -empty )
do
  echo $dir
  grep [0-9] $dir
#  rm -rf $file
done | sort > "$LOG"

Assuming there are only subdirectories in $DIRECTORY that start with "fs", this should work:

find $DIRECTORY/fs*/* -type d -printf "'%p'\n"|sort -r |xargs rmdir 2>&-

There are directories under, so this doesn't work. The directories look like this:
/directory/images/fsa/09005573FRA
/directory/images/fsa/09004364EVA

It is these 0900.... directories that need to be removed.
There a literally hundreds of these subdirectories that I need to remove. I guess my question wasn't clear enough. Can you still help me?

Actually I think that should work. You seem to confirm that there are only subdirectories called fs* (e.g. fsa) in $DIRECTORY (/directory/images). These subdirectories must not be removed but the subdirectories inside these subdirectories do have to be removed if they are empty (i.e. contain no files or further subdirectories).

S.

After review, I believe you are right. Thanks,