diff --git a/ci/lib-travisci.sh b/ci/lib-travisci.sh
index 1efee55ef7..109ef280da 100755
--- a/ci/lib-travisci.sh
+++ b/ci/lib-travisci.sh
@@ -97,7 +97,7 @@ fi
 export DEVELOPER=1
 export DEFAULT_TEST_TARGET=prove
 export GIT_PROVE_OPTS="--timer --jobs 3 --state=failed,slow,save"
-export GIT_TEST_OPTS="--verbose-log"
+export GIT_TEST_OPTS="--verbose-log -x"
 export GIT_TEST_CLONE_2GB=YesPlease
 
 case "$jobname" in
diff --git a/t/README b/t/README
index 1a1361a806..24ddebfabf 100644
--- a/t/README
+++ b/t/README
@@ -84,9 +84,10 @@ appropriately before running "make".
 
 -x::
 	Turn on shell tracing (i.e., `set -x`) during the tests
-	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.
+	themselves. Implies `--verbose`.
+	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::
@@ -452,6 +453,22 @@ Don't:
    causing the next test to start in an unexpected directory.  Do so
    inside a subshell if necessary.
 
+ - save and verify the standard error of compound commands, i.e. group
+   commands, subshells, and shell functions (except test helper
+   functions like 'test_must_fail') like this:
+
+     ( cd dir && git cmd ) 2>error &&
+     test_cmp expect error
+
+   When running the test with '-x' tracing, then the trace of commands
+   executed in the compound command will be included in standard error
+   as well, quite possibly throwing off the subsequent checks examining
+   the output.  Instead, save only the relevant git command's standard
+   error:
+
+     ( cd dir && git cmd 2>../error ) &&
+     test_cmp expect error
+
  - Break the TAP output
 
    The raw output from your test may be interpreted by a TAP harness. TAP
diff --git a/t/lib-terminal.sh b/t/lib-terminal.sh
index cd220e378e..e3809dcead 100644
--- a/t/lib-terminal.sh
+++ b/t/lib-terminal.sh
@@ -9,8 +9,8 @@ test_terminal () {
 		echo >&4 "test_terminal: need to declare TTY prerequisite"
 		return 127
 	fi
-	perl "$TEST_DIRECTORY"/test-terminal.perl "$@"
-}
+	perl "$TEST_DIRECTORY"/test-terminal.perl "$@" 2>&7
+} 7>&2 2>&4
 
 test_lazy_prereq TTY '
 	test_have_prereq PERL &&
diff --git a/t/t1507-rev-parse-upstream.sh b/t/t1507-rev-parse-upstream.sh
index b23c4e3fab..2ce68cc277 100755
--- a/t/t1507-rev-parse-upstream.sh
+++ b/t/t1507-rev-parse-upstream.sh
@@ -42,7 +42,7 @@ commit_subject () {
 
 error_message () {
 	(cd clone &&
-	 test_must_fail git rev-parse --verify "$@")
+	 test_must_fail git rev-parse --verify "$@" 2>../error)
 }
 
 test_expect_success '@{upstream} resolves to correct full name' '
@@ -159,8 +159,8 @@ test_expect_success 'branch@{u} error message when no upstream' '
 	cat >expect <<-EOF &&
 	fatal: no upstream configured for branch ${sq}non-tracking${sq}
 	EOF
-	error_message non-tracking@{u} 2>actual &&
-	test_i18ncmp expect actual
+	error_message non-tracking@{u} &&
+	test_i18ncmp expect error
 '
 
 test_expect_success '@{u} error message when no upstream' '
@@ -175,8 +175,8 @@ test_expect_success 'branch@{u} error message with misspelt branch' '
 	cat >expect <<-EOF &&
 	fatal: no such branch: ${sq}no-such-branch${sq}
 	EOF
-	error_message no-such-branch@{u} 2>actual &&
-	test_i18ncmp expect actual
+	error_message no-such-branch@{u} &&
+	test_i18ncmp expect error
 '
 
 test_expect_success '@{u} error message when not on a branch' '
@@ -192,8 +192,8 @@ test_expect_success 'branch@{u} error message if upstream branch not fetched' '
 	cat >expect <<-EOF &&
 	fatal: upstream branch ${sq}refs/heads/side${sq} not stored as a remote-tracking branch
 	EOF
-	error_message bad-upstream@{u} 2>actual &&
-	test_i18ncmp expect actual
+	error_message bad-upstream@{u} &&
+	test_i18ncmp expect error
 '
 
 test_expect_success 'pull works when tracking a local branch' '
diff --git a/t/t1510-repo-setup.sh b/t/t1510-repo-setup.sh
index 13ae12dfa7..e6854b828e 100755
--- a/t/t1510-repo-setup.sh
+++ b/t/t1510-repo-setup.sh
@@ -39,6 +39,10 @@ A few rules for repo setup:
 11. When user's cwd is outside worktree, cwd remains unchanged,
     prefix is NULL.
 "
+
+# This test heavily relies on the standard error of nested function calls.
+test_untraceable=UnfortunatelyYes
+
 . ./test-lib.sh
 
 here=$(pwd)
diff --git a/t/t3030-merge-recursive.sh b/t/t3030-merge-recursive.sh
index cdc38fe5d1..3563e77b37 100755
--- a/t/t3030-merge-recursive.sh
+++ b/t/t3030-merge-recursive.sh
@@ -525,20 +525,22 @@ test_expect_success 'merge-recursive w/ empty work tree - ours has rename' '
 		GIT_INDEX_FILE="$PWD/ours-has-rename-index" &&
 		export GIT_INDEX_FILE &&
 		mkdir "$GIT_WORK_TREE" &&
-		git read-tree -i -m $c7 &&
-		git update-index --ignore-missing --refresh &&
-		git merge-recursive $c0 -- $c7 $c3 &&
-		git ls-files -s >actual-files
-	) 2>actual-err &&
-	>expected-err &&
+		git read-tree -i -m $c7 2>actual-err &&
+		test_must_be_empty actual-err &&
+		git update-index --ignore-missing --refresh 2>actual-err &&
+		test_must_be_empty actual-err &&
+		git merge-recursive $c0 -- $c7 $c3 2>actual-err &&
+		test_must_be_empty actual-err &&
+		git ls-files -s >actual-files 2>actual-err &&
+		test_must_be_empty actual-err
+	) &&
 	cat >expected-files <<-EOF &&
 	100644 $o3 0	b/c
 	100644 $o0 0	c
 	100644 $o0 0	d/e
 	100644 $o0 0	e
 	EOF
-	test_cmp expected-files actual-files &&
-	test_cmp expected-err actual-err
+	test_cmp expected-files actual-files
 '
 
 test_expect_success 'merge-recursive w/ empty work tree - theirs has rename' '
@@ -548,20 +550,22 @@ test_expect_success 'merge-recursive w/ empty work tree - theirs has rename' '
 		GIT_INDEX_FILE="$PWD/theirs-has-rename-index" &&
 		export GIT_INDEX_FILE &&
 		mkdir "$GIT_WORK_TREE" &&
-		git read-tree -i -m $c3 &&
-		git update-index --ignore-missing --refresh &&
-		git merge-recursive $c0 -- $c3 $c7 &&
-		git ls-files -s >actual-files
-	) 2>actual-err &&
-	>expected-err &&
+		git read-tree -i -m $c3 2>actual-err &&
+		test_must_be_empty actual-err &&
+		git update-index --ignore-missing --refresh 2>actual-err &&
+		test_must_be_empty actual-err &&
+		git merge-recursive $c0 -- $c3 $c7 2>actual-err &&
+		test_must_be_empty actual-err &&
+		git ls-files -s >actual-files 2>actual-err &&
+		test_must_be_empty actual-err
+	) &&
 	cat >expected-files <<-EOF &&
 	100644 $o3 0	b/c
 	100644 $o0 0	c
 	100644 $o0 0	d/e
 	100644 $o0 0	e
 	EOF
-	test_cmp expected-files actual-files &&
-	test_cmp expected-err actual-err
+	test_cmp expected-files actual-files
 '
 
 test_expect_success 'merge removes empty directories' '
diff --git a/t/t5500-fetch-pack.sh b/t/t5500-fetch-pack.sh
index ec9ba9bf6e..0680dec808 100755
--- a/t/t5500-fetch-pack.sh
+++ b/t/t5500-fetch-pack.sh
@@ -482,24 +482,24 @@ test_expect_success 'set up tests of missing reference' '
 test_expect_success 'test lonely missing ref' '
 	(
 		cd client &&
-		test_must_fail git fetch-pack --no-progress .. refs/heads/xyzzy
-	) >/dev/null 2>error-m &&
+		test_must_fail git fetch-pack --no-progress .. refs/heads/xyzzy 2>../error-m
+	) &&
 	test_i18ncmp expect-error error-m
 '
 
 test_expect_success 'test missing ref after existing' '
 	(
 		cd client &&
-		test_must_fail git fetch-pack --no-progress .. refs/heads/A refs/heads/xyzzy
-	) >/dev/null 2>error-em &&
+		test_must_fail git fetch-pack --no-progress .. refs/heads/A refs/heads/xyzzy 2>../error-em
+	) &&
 	test_i18ncmp expect-error error-em
 '
 
 test_expect_success 'test missing ref before existing' '
 	(
 		cd client &&
-		test_must_fail git fetch-pack --no-progress .. refs/heads/xyzzy refs/heads/A
-	) >/dev/null 2>error-me &&
+		test_must_fail git fetch-pack --no-progress .. refs/heads/xyzzy refs/heads/A 2>../error-me
+	) &&
 	test_i18ncmp expect-error error-me
 '
 
diff --git a/t/t5526-fetch-submodules.sh b/t/t5526-fetch-submodules.sh
index 74486c73b0..9cc4b569c0 100755
--- a/t/t5526-fetch-submodules.sh
+++ b/t/t5526-fetch-submodules.sh
@@ -85,7 +85,7 @@ test_expect_success "fetch --recurse-submodules -j2 has the same output behaviou
 	add_upstream_commit &&
 	(
 		cd downstream &&
-		GIT_TRACE=$(pwd)/../trace.out git fetch --recurse-submodules -j2 2>../actual.err
+		GIT_TRACE="$TRASH_DIRECTORY/trace.out" git fetch --recurse-submodules -j2 2>../actual.err
 	) &&
 	test_must_be_empty actual.out &&
 	test_i18ncmp expect.err actual.err &&
diff --git a/t/t5570-git-daemon.sh b/t/t5570-git-daemon.sh
index 755b05a8ae..0d4c52016b 100755
--- a/t/t5570-git-daemon.sh
+++ b/t/t5570-git-daemon.sh
@@ -50,7 +50,7 @@ test_expect_success 'no-op fetch -v stderr is as expected' '
 '
 
 test_expect_success 'no-op fetch without "-v" is quiet' '
-	(cd clone && git fetch) 2>stderr &&
+	(cd clone && git fetch 2>../stderr) &&
 	! test -s stderr
 '
 
diff --git a/t/t9903-bash-prompt.sh b/t/t9903-bash-prompt.sh
index 97c9b32c2e..8f5c811dd7 100755
--- a/t/t9903-bash-prompt.sh
+++ b/t/t9903-bash-prompt.sh
@@ -735,22 +735,12 @@ test_expect_success 'prompt - hide if pwd ignored - env var set, config unset, p
 	test_cmp expected "$actual"
 '
 
-test_expect_success 'prompt - hide if pwd ignored - inside gitdir (stdout)' '
+test_expect_success 'prompt - hide if pwd ignored - inside gitdir' '
 	printf " (GIT_DIR!)" >expected &&
 	(
 		GIT_PS1_HIDE_IF_PWD_IGNORED=y &&
 		cd .git &&
-		__git_ps1 >"$actual" 2>/dev/null
-	) &&
-	test_cmp expected "$actual"
-'
-
-test_expect_success 'prompt - hide if pwd ignored - inside gitdir (stderr)' '
-	printf "" >expected &&
-	(
-		GIT_PS1_HIDE_IF_PWD_IGNORED=y &&
-		cd .git &&
-		__git_ps1 >/dev/null 2>"$actual"
+		__git_ps1 >"$actual"
 	) &&
 	test_cmp expected "$actual"
 '
diff --git a/t/test-lib-functions.sh b/t/test-lib-functions.sh
index 6e342804f9..b895366fee 100644
--- a/t/test-lib-functions.sh
+++ b/t/test-lib-functions.sh
@@ -629,7 +629,7 @@ test_must_fail () {
 		_test_ok=
 		;;
 	esac
-	"$@"
+	"$@" 2>&7
 	exit_code=$?
 	if test $exit_code -eq 0 && ! list_contains "$_test_ok" success
 	then
@@ -652,7 +652,7 @@ test_must_fail () {
 		return 1
 	fi
 	return 0
-}
+} 7>&2 2>&4
 
 # Similar to test_must_fail, but tolerates success, too.  This is
 # meant to be used in contexts like:
@@ -668,8 +668,8 @@ test_must_fail () {
 # Accepts the same options as test_must_fail.
 
 test_might_fail () {
-	test_must_fail ok=success "$@"
-}
+	test_must_fail ok=success "$@" 2>&7
+} 7>&2 2>&4
 
 # Similar to test_must_fail and test_might_fail, but check that a
 # given command exited with a given exit code. Meant to be used as:
@@ -681,7 +681,7 @@ test_might_fail () {
 test_expect_code () {
 	want_code=$1
 	shift
-	"$@"
+	"$@" 2>&7
 	exit_code=$?
 	if test $exit_code = $want_code
 	then
@@ -690,7 +690,7 @@ test_expect_code () {
 
 	echo >&4 "test_expect_code: command exited with $exit_code, we wanted $want_code $*"
 	return 1
-}
+} 7>&2 2>&4
 
 # test_cmp is a helper function to compare actual and expected output.
 # You can use it like:
@@ -896,8 +896,8 @@ test_write_lines () {
 }
 
 perl () {
-	command "$PERL_PATH" "$@"
-}
+	command "$PERL_PATH" "$@" 2>&7
+} 7>&2 2>&4
 
 # Is the value one of the various ways to spell a boolean true/false?
 test_normalize_bool () {
@@ -1037,13 +1037,13 @@ test_env () {
 				shift
 				;;
 			*)
-				"$@"
+				"$@" 2>&7
 				exit
 				;;
 			esac
 		done
 	)
-}
+} 7>&2 2>&4
 
 # Returns true if the numeric exit code in "$2" represents the expected signal
 # in "$1". Signals should be given numerically.
@@ -1085,9 +1085,9 @@ nongit () {
 		GIT_CEILING_DIRECTORIES=$(pwd) &&
 		export GIT_CEILING_DIRECTORIES &&
 		cd non-repo &&
-		"$@"
+		"$@" 2>&7
 	)
-}
+} 7>&2 2>&4
 
 # convert stdin to pktline representation; note that empty input becomes an
 # empty packet, not a flush packet (for that you can just print 0000 yourself).
diff --git a/t/test-lib.sh b/t/test-lib.sh
index 9535d2e0a9..7740d511d2 100644
--- a/t/test-lib.sh
+++ b/t/test-lib.sh
@@ -264,7 +264,24 @@ 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