diff --git a/t/README b/t/README
index b3f7b449c3..c430e9c52c 100644
--- a/t/README
+++ b/t/README
@@ -87,6 +87,9 @@ appropriately before running "make".
 	themselves. Implies `--verbose`. Note that in non-bash shells,
 	this can cause failures in some tests which redirect and test
 	the output of shell functions. Use with caution.
+	Ignored in test scripts that set the variable 'test_untraceable'
+	to a non-empty value, unless it's run with a Bash version
+	supporting BASH_XTRACEFD, i.e. v4.1 or later.
 
 -d::
 --debug::
diff --git a/t/test-lib.sh b/t/test-lib.sh
index 33f6ce26f6..732213ef1b 100644
--- a/t/test-lib.sh
+++ b/t/test-lib.sh
@@ -263,7 +263,24 @@ do
 		GIT_TEST_CHAIN_LINT=0
 		shift ;;
 	-x)
-		trace=t
+		# Some test scripts can't be reliably traced  with '-x',
+		# unless the test is run with a Bash version supporting
+		# BASH_XTRACEFD (introduced in Bash v4.1).  Check whether
+		# this test is marked as such, and ignore '-x' if it
+		# isn't executed with a suitable Bash version.
+		if test -z "$test_untraceable" || {
+		     test -n "$BASH_VERSION" && {
+		       test ${BASH_VERSINFO[0]} -gt 4 || {
+			 test ${BASH_VERSINFO[0]} -eq 4 &&
+			 test ${BASH_VERSINFO[1]} -ge 1
+		       }
+		     }
+		   }
+		then
+			trace=t
+		else
+			echo >&2 "warning: ignoring -x; '$0' is untraceable without BASH_XTRACEFD"
+		fi
 		shift ;;
 	--verbose-log)
 		verbose_log=t