diff --git a/tools/cldr/lib/README.txt b/tools/cldr/lib/README.txt
index 66df9c6232c..abd9b2b0ffd 100644
--- a/tools/cldr/lib/README.txt
+++ b/tools/cldr/lib/README.txt
@@ -41,7 +41,7 @@ doesn't work on your system.
 To regenerate the CLDR API jar you need to build the "jar" target manually
 using the Ant build.xml file in the "tools/java" directory of the CLDR project:
 
-$ cd <CLDR_ROOT>/tools/java
+$ cd "$CLDR_ROOT/tools/java"
 $ ant clean jar
 
 This should result in the cldr.jar file being built into that directory, which
@@ -62,7 +62,7 @@ $ mvn install:install-file \
   -Dpackaging=jar \
   -DgeneratePom=true \
   -DlocalRepositoryPath=. \
-  -Dfile=<CLDR_ROOT>/tools/java/cldr.jar
+  -Dfile="$CLDR_ROOT/tools/java/cldr.jar"
 
 And if you have updated one of these libraries then from this directory run:
 
diff --git a/tools/cldr/lib/install-cldr-jars.sh b/tools/cldr/lib/install-cldr-jars.sh
index 7b630643990..ab9501e4848 100755
--- a/tools/cldr/lib/install-cldr-jars.sh
+++ b/tools/cldr/lib/install-cldr-jars.sh
@@ -15,6 +15,12 @@
 # Usage (from the directory of this script):
 #
 # ./install-cldr-jars.sh <CLDR-root-directory>
+#
+# Note to maintainers: This script cannot be assumed to run on a Unix/Linux
+# based system, and while a Posix compliant bash shell is required, any
+# assumptions about auxiliary Unix tools should be minimized (e.g. things
+# like "dirname" or "tempfile" may not exist). Where bash-only alternatives
+# have to be used, they should be clearly documented.
 
 # Exit with a message for fatal errors.
 function die() {
@@ -28,35 +34,28 @@ function die() {
 function run_with_logging() {
   echo >> "${LOG_FILE}"
   echo "Running: ${@}" >> "${LOG_FILE}"
-  echo "----------------------------------------------------------------" >> "${LOG_FILE}"
+  echo -- "----------------------------------------------------------------" >> "${LOG_FILE}"
   "${@}" >> "${LOG_FILE}" 2>&1
   if (( $? != 0 )) ; then
-    echo "---- Previous command failed ----" >> "${LOG_FILE}"
+    echo -- "---- Previous command failed ----" >> "${LOG_FILE}"
     echo "Error running: ${@}"
     read -p "Show log file? " -n 1 -r
     echo
     if [[ "${REPLY}" =~ ^[Yy]$ ]] ; then
       less -X "${LOG_FILE}"
     fi
-    mv -f "${LOG_FILE}" "${ROOT_DIR}/last_log.txt"
-    echo "Log file: ${ROOT_DIR}/last_log.txt"
+    echo "Log file: ${LOG_FILE}"
     exit 1
   fi
-  echo "---- Previous command succeeded ----" >> "${LOG_FILE}"
+  echo -- "---- Previous command succeeded ----" >> "${LOG_FILE}"
 }
 
 # First require that we are run from the same directory as the script.
-ROOT_DIR="$(realpath $(dirname $0))"
-if [[ "${ROOT_DIR}" != "$(realpath ${PWD})" ]] ; then
-  echo "WARNING: Shell script should be run from the Maven lib/ directory"
-  echo "Current directory:"
-  echo "  ${PWD}"
-  echo "Maven lib/ direcory (where this script is):"
-  echo "  ${ROOT_DIR}"
-  read -p "Change to lib/ directory and continue? " -n 1 -r
-  echo
-  [[ "${REPLY}" =~ ^[Yy]$ ]] || die "Script must be run from the Maven lib/ directory"
-  cd "$ROOT_DIR"
+# Can't assume users have "dirname" available so hack it a bit with shell
+# substitution (if no directory path was prepended, SCRIPT_DIR==$0).
+SCRIPT_DIR=${0%/*}
+if [[ "$SCRIPT_DIR" != "$0" ]] ; then
+  cd $SCRIPT_DIR
 fi
 
 # Check for some expected environmental things early.
@@ -67,9 +66,10 @@ which mvn > /dev/null || die "Cannot find Maven executable 'mvn' in the current
 (( $# == 1 )) && [[ -d "$1" ]] || die "Usage: ./install-cldr-jars.sh <CLDR-root-directory>"
 
 # Set up a log file (and be nice about tidying it up).
-LOG_FILE="$(tempfile)" || die "Cannot create temporary file!"
-trap "rm -f -- '${LOG_FILE}'" EXIT
-echo "---- LOG FILE ---- $(date '+%F %T') ----" >> "${LOG_FILE}"
+# Cannot assume "tempfile" exists so use a timestamp (we expect "date" to exist though).
+LOG_FILE="${TMPDIR:-/tmp}/cldr2icu_log_$(date '+%m%d_%H%M%S').txt"
+touch $LOG_FILE || die "Cannot create temporary file: ${LOG_FILE}"
+echo -- "---- LOG FILE ---- $(date '+%F %T') ----" >> "${LOG_FILE}"
 
 # Build the cldr.jar in the CLDR tools directory.
 CLDR_TOOLS_DIR="$1/tools/java"
@@ -98,6 +98,5 @@ run_with_logging mvn -B dependency:purge-local-repository \
   -Dproject.parent.relativePath="" \
   -DmanualIncludes=org.unicode.cldr:cldr-api:jar 
 
-mv -f "${LOG_FILE}" "last_log.txt"
-echo "All done! (log file: last_log.txt)"
-trap - EXIT
+echo "All done!"
+echo "Log file: ${LOG_FILE}"