diff --git a/tests/check.mk b/tests/check.mk
index df0c92467..1391d516b 100644
--- a/tests/check.mk
+++ b/tests/check.mk
@@ -49,7 +49,8 @@ built_programs = \
 # variables to test scripts.
 TESTS_ENVIRONMENT =				\
   . $(srcdir)/lang-default;			\
-  tmp__=$$TMPDIR; test -d "$$tmp__" || tmp__=.;	\
+  tmp__=$${TMPDIR-/tmp};			\
+  test -d "$$tmp__" && test -w "$$tmp__" || tmp__=.;	\
   . $(srcdir)/envvar-check;			\
   TMPDIR=$$tmp__; export TMPDIR;		\
   exec 9>&2;					\
diff --git a/tests/misc/sort-compress b/tests/misc/sort-compress
index a51a2df7c..50845c9e2 100755
--- a/tests/misc/sort-compress
+++ b/tests/misc/sort-compress
@@ -22,9 +22,6 @@ print_ver_ sort
 seq -w 2000 > exp || framework_failure
 tac exp > in || framework_failure
 
-# Ensure that $TMPDIR is valid.
-TMPDIR=.; export TMPDIR
-
 # This should force the use of temp files
 sort -S 1k in > out || fail=1
 compare exp out || fail=1
diff --git a/tests/misc/sort-compress-proc b/tests/misc/sort-compress-proc
index 8d0094f13..30f6b43b1 100755
--- a/tests/misc/sort-compress-proc
+++ b/tests/misc/sort-compress-proc
@@ -20,13 +20,6 @@
 print_ver_ sort
 expensive_
 
-# Ensure that $TMPDIR is valid.
-if test -d /tmp && test -w /tmp
-then TMPDIR=/tmp
-else TMPDIR=.
-fi
-export TMPDIR
-
 seq -w 2000 > exp || fail=1
 tac exp > in || fail=1
 insize=$(stat -c %s - <in) || fail=1
@@ -78,10 +71,13 @@ rm -f ok
 
 rm -f compress
 
-# Give compression subprocesses time to react when 'sort' exits.
+# If $TMPDIR is relative, give subprocesses time to react when 'sort' exits.
 # Otherwise, under NFS, when 'sort' unlinks the temp files and they
 # are renamed to .nfsXXXX instead of being removed, the parent cleanup
 # of this directory will fail because the files are still open.
-sleep 1
+case $TMPDIR in
+/*) ;;
+*) sleep 1;;
+esac
 
 Exit $fail