diff --git a/regress/valgrind-unit.sh b/regress/valgrind-unit.sh
index d1c110008..4143ead4b 100755
--- a/regress/valgrind-unit.sh
+++ b/regress/valgrind-unit.sh
@@ -7,11 +7,9 @@ UNIT_ARGS="$@"
 test "x$OBJ" = "x" && OBJ=$PWD
 
 # This mostly replicates the logic in test-exec.sh for running the
-# regress tests under valgrind.
-VG_LEAK="--leak-check=no"
-if [ x"$VALGRIND_CHECK_LEAKS" != "x" ]; then
-	VG_LEAK="--leak-check=full"
-fi
+# regress tests under valgrind, except that we unconditionally enable
+# leak checking because the unit tests should be clean.
+VG_LEAK="--leak-check=full"
 VG_TEST=`basename $UNIT_BINARY`
 VG_LOG="$OBJ/valgrind-out/${VG_TEST}.%p"
 VG_OPTS="--track-origins=yes $VG_LEAK --log-file=${VG_LOG}"