diff --git a/tests/shared_test_functions.sh b/tests/shared_test_functions.sh
index ff4fa310..db06204a 100644
--- a/tests/shared_test_functions.sh
+++ b/tests/shared_test_functions.sh
@@ -26,6 +26,8 @@
 #   Set up the below variables.
 # - expected_exitcode(expected, actual):
 #   Check if ${expected} matches ${actual}.
+# - get_filelist (pattern): return a sorted list of files corresponding to
+#   ${pattern}, separated by newlines.
 # - run_scenarios():
 #   Run scenarios in the test directory.
 #
@@ -205,6 +207,29 @@ expected_exitcode() {
 	fi
 }
 
+## get_filelist (pattern):
+# Return a sorted list of files corresponding to ${pattern}, separated by
+# newlines.
+get_filelist() {
+	_get_filelist_pattern=$1
+
+	# Separate the pattern into directory and basename.
+	_get_filelist_dir=$(dirname "${_get_filelist_pattern}")
+	_get_filelist_base=$(basename "${_get_filelist_pattern}")
+
+	# Find all files matching the pattern.  Don't complain if the
+	# directory does not exist (i.e. checking for non-existent valgrind
+	# logfiles).
+	_get_filelist_unsorted=$(find "${_get_filelist_dir}"		\
+	    -name "${_get_filelist_base}" -prune -print 2>/dev/null)
+
+	# Sort the list.
+	_get_filelist_filelist=$(printf "%s" "${_get_filelist_unsorted}" | sort)
+
+	# Return the sorted list.
+	printf "%s" "${_get_filelist_filelist}"
+}
+
 ## notify_success_or_fail (log_basename, val_log_basename):
 # Examine all "exit code" files beginning with ${log_basename} and
 # print "SUCCESS!", "FAILED!", "SKIP!", or "PARTIAL SUCCESS / SKIP!"
@@ -217,7 +242,7 @@ notify_success_or_fail() {
 	val_log_basename=$2
 
 	# Bail if there's no exitfiles.
-	exitfiles=$(ls "${log_basename}"-*.exit) || true
+	exitfiles=$(set -o noglob; get_filelist "${log_basename}"-*.exit)
 	if [ -z "${exitfiles}" ]; then
 		echo "FAILED" 1>&2
 		s_retval=1
@@ -229,7 +254,7 @@ notify_success_or_fail() {
 	skip_exitfiles=0
 
 	# Check each exitfile.
-	for exitfile in $(echo "${exitfiles}" | sort); do
+	for exitfile in ${exitfiles}; do
 		ret=$(cat "${exitfile}")
 		total_exitfiles=$(( total_exitfiles + 1 ))
 		if [ "${ret}" -lt 0 ]; then
diff --git a/tests/shared_valgrind_functions.sh b/tests/shared_valgrind_functions.sh
index e4e9033b..f73b9d3f 100644
--- a/tests/shared_valgrind_functions.sh
+++ b/tests/shared_valgrind_functions.sh
@@ -327,7 +327,7 @@ valgrind_check_basenames() {
 	val_basename=$(valgrind_get_basename "${exitfile}")
 
 	# Get list of files to check.  (Yes, the star goes outside the quotes.)
-	logfiles=$(ls "${val_basename}"* 2>/dev/null)
+	logfiles=$(set -o noglob; get_filelist "${val_basename}"*)
 	num_logfiles=$(echo "${logfiles}" | wc -w)
 
 	# Bail if we don't have any valgrind logfiles to check.