diff --git a/ci/run-build-and-tests.sh b/ci/run-build-and-tests.sh
index e2d783d90b..1d9a0a736d 100755
--- a/ci/run-build-and-tests.sh
+++ b/ci/run-build-and-tests.sh
@@ -10,7 +10,14 @@ export TEST_CONTRIB_TOO=yes
 case "$jobname" in
 linux-musl-meson)
 	MESONFLAGS="$MESONFLAGS -Drust=disabled"
+	export GIT_TEST_USE_SET_E=yes
 	;;
+almalinux-*|debian-*|fedora-*|linux-*)
+	export GIT_TEST_USE_SET_E=yes
+	;;
+esac
+
+case "$jobname" in
 fedora-breaking-changes-musl|linux-breaking-changes)
 	export WITH_BREAKING_CHANGES=YesPlease
 	MESONFLAGS="$MESONFLAGS -Dbreaking_changes=true"
diff --git a/t/lib-git-daemon.sh b/t/lib-git-daemon.sh
index e62569222b..d172aa51f0 100644
--- a/t/lib-git-daemon.sh
+++ b/t/lib-git-daemon.sh
@@ -85,14 +85,16 @@ stop_git_daemon() {
 
 	# kill git-daemon child of git
 	say >&3 "Stopping git daemon ..."
+
 	kill "$GIT_DAEMON_PID"
-	wait "$GIT_DAEMON_PID" >&3 2>&4
-	ret=$?
+	ret=0; wait "$GIT_DAEMON_PID" >&3 2>&4 || ret=$?
+
 	if ! test_match_signal 15 $ret
 	then
 		error "git daemon exited with status: $ret"
 	fi
-	kill "$(cat "$GIT_DAEMON_PIDFILE")" 2>/dev/null
+
+	kill "$(cat "$GIT_DAEMON_PIDFILE")" 2>/dev/null || :
 	GIT_DAEMON_PID=
 	rm -f git_daemon_output "$GIT_DAEMON_PIDFILE"
 }
diff --git a/t/lib-git-svn.sh b/t/lib-git-svn.sh
index 2fde2353fd..52843f667d 100644
--- a/t/lib-git-svn.sh
+++ b/t/lib-git-svn.sh
@@ -15,8 +15,7 @@ GIT_SVN_DIR=$GIT_DIR/svn/refs/remotes/git-svn
 SVN_TREE=$GIT_SVN_DIR/svn-tree
 test_set_port SVNSERVE_PORT
 
-svn >/dev/null 2>&1
-if test $? -ne 1
+if ! svn help >/dev/null 2>&1
 then
 	skip_all='skipping git svn tests, svn not found'
 	test_done
@@ -27,13 +26,13 @@ export svnrepo
 svnconf=$PWD/svnconf
 export svnconf
 
+x=0
 perl -w -e "
 use SVN::Core;
 use SVN::Repos;
 \$SVN::Core::VERSION gt '1.1.0' or exit(42);
 system(qw/svnadmin create --fs-type fsfs/, \$ENV{svnrepo}) == 0 or exit(41);
-" >&3 2>&4
-x=$?
+" >&3 2>&4 || x=$?
 if test $x -ne 0
 then
 	if test $x -eq 42; then
diff --git a/t/lib-httpd.sh b/t/lib-httpd.sh
index 4c76e813e3..fc646447d5 100644
--- a/t/lib-httpd.sh
+++ b/t/lib-httpd.sh
@@ -235,11 +235,10 @@ start_httpd() {
 
 	test_atexit stop_httpd
 
-	"$LIB_HTTPD_PATH" -d "$HTTPD_ROOT_PATH" \
+	if ! "$LIB_HTTPD_PATH" -d "$HTTPD_ROOT_PATH" \
 		-f "$TEST_PATH/apache.conf" $HTTPD_PARA \
 		-c "Listen 127.0.0.1:$LIB_HTTPD_PORT" -k start \
 		>&3 2>&4
-	if test $? -ne 0
 	then
 		cat "$HTTPD_ROOT_PATH"/error.log >&4 2>/dev/null
 		test_skip_or_die GIT_TEST_HTTPD "web server setup failed"
diff --git a/t/t0005-signals.sh b/t/t0005-signals.sh
index afba0fc3fc..84319cf169 100755
--- a/t/t0005-signals.sh
+++ b/t/t0005-signals.sh
@@ -42,12 +42,12 @@ test_expect_success 'create blob' '
 '
 
 test_expect_success !MINGW 'a constipated git dies with SIGPIPE' '
-	OUT=$( ((large_git; echo $? 1>&3) | :) 3>&1 ) &&
+	OUT=$( ((large_git && echo 0 1>&3 || echo $? 1>&3) | :) 3>&1 ) &&
 	test_match_signal 13 "$OUT"
 '
 
 test_expect_success !MINGW 'a constipated git dies with SIGPIPE even if parent ignores it' '
-	OUT=$( ((trap "" PIPE && large_git; echo $? 1>&3) | :) 3>&1 ) &&
+	OUT=$( ((trap "" PIPE && large_git && echo 0 1>&3 || echo $? 1>&3) | :) 3>&1 ) &&
 	test_match_signal 13 "$OUT"
 '
 
diff --git a/t/t0008-ignores.sh b/t/t0008-ignores.sh
index e716b5cdfa..d77a179bdd 100755
--- a/t/t0008-ignores.sh
+++ b/t/t0008-ignores.sh
@@ -122,8 +122,8 @@ test_expect_success_multiple () {
 	fi
 	testname="$1" expect_all="$2" code="$3"
 
-	expect_verbose=$( echo "$expect_all" | grep -v '^::	' )
-	expect=$( echo "$expect_verbose" | sed -e 's/.*	//' )
+	expect_verbose=$(echo "$expect_all" | grep -v '^::	' || :)
+	expect=$(echo "$expect_verbose" | sed -e 's/.*	//')
 
 	test_expect_success $prereq "$testname${no_index_opt:+ with $no_index_opt}" '
 		expect "$expect" &&
diff --git a/t/t1301-shared-repo.sh b/t/t1301-shared-repo.sh
index 630a47af21..0e0d07a1a1 100755
--- a/t/t1301-shared-repo.sh
+++ b/t/t1301-shared-repo.sh
@@ -12,7 +12,7 @@ TEST_CREATE_REPO_NO_TEMPLATE=1
 . ./test-lib.sh
 
 # Remove a default ACL from the test dir if possible.
-setfacl -k . 2>/dev/null
+setfacl -k . 2>/dev/null || :
 
 # User must have read permissions to the repo -> failure on --shared=0400
 test_expect_success 'shared = 0400 (faulty permission u-w)' '
diff --git a/t/t3600-rm.sh b/t/t3600-rm.sh
index 1f16e6b522..a371ea690e 100755
--- a/t/t3600-rm.sh
+++ b/t/t3600-rm.sh
@@ -260,7 +260,7 @@ test_expect_success 'choking "git rm" should not let it die with cruft (induce S
 
 test_expect_success !MINGW 'choking "git rm" should not let it die with cruft (induce and check SIGPIPE)' '
 	choke_git_rm_setup &&
-	OUT=$( ((trap "" PIPE && git rm -n "some-file-*"; echo $? 1>&3) | :) 3>&1 ) &&
+	OUT=$( ((trap "" PIPE && git rm -n "some-file-*" && echo 0 1>&3 || echo $? 1>&3) | :) 3>&1 ) &&
 	test_match_signal 13 "$OUT" &&
 	test_path_is_missing .git/index.lock
 '
diff --git a/t/t3901-i18n-patch.sh b/t/t3901-i18n-patch.sh
index f03601b49a..ef7d7e1edc 100755
--- a/t/t3901-i18n-patch.sh
+++ b/t/t3901-i18n-patch.sh
@@ -28,7 +28,8 @@ check_encoding () {
 		8859)
 			grep "^encoding ISO8859-1" ;;
 		*)
-			grep "^encoding ISO8859-1"; test "$?" != 0 ;;
+			ret=0; grep "^encoding ISO8859-1" || ret=$?
+			test "$ret" != 0 ;;
 		esac || return 1
 		j=$i
 		i=$(($i+1))
diff --git a/t/t4032-diff-inter-hunk-context.sh b/t/t4032-diff-inter-hunk-context.sh
index bada0cbd32..2d216fb70f 100755
--- a/t/t4032-diff-inter-hunk-context.sh
+++ b/t/t4032-diff-inter-hunk-context.sh
@@ -17,7 +17,7 @@ f() {
 
 t() {
 	use_config=
-	git config --unset diff.interHunkContext
+	git config --unset diff.interHunkContext || :
 
 	case $# in
 	4) hunks=$4; cmd="diff -U$3";;
@@ -40,11 +40,13 @@ t() {
 		test $(git $cmd $file | grep '^@@ ' | wc -l) = $hunks
 	"
 
-	test -f $expected &&
-	test_expect_success "$label: check output" "
-		git $cmd $file | grep -v '^index ' >actual &&
-		test_cmp $expected actual
-	"
+	if test -f $expected
+	then
+		test_expect_success "$label: check output" "
+			git $cmd $file | grep -v '^index ' >actual &&
+			test_cmp $expected actual
+		"
+	fi
 }
 
 cat <<EOF >expected.f1.0.1 || exit 1
diff --git a/t/t5000-tar-tree.sh b/t/t5000-tar-tree.sh
index 5465054f17..a8c28533dc 100755
--- a/t/t5000-tar-tree.sh
+++ b/t/t5000-tar-tree.sh
@@ -503,8 +503,8 @@ test_expect_success LONG_IS_64BIT 'set up repository with huge blob' '
 # would generate the whole 64GB).
 test_expect_success LONG_IS_64BIT 'generate tar with huge size' '
 	{
-		git archive HEAD
-		echo $? >exit-code
+		{ ret=0 && git archive HEAD || ret=$?; } &&
+		echo "$ret" >exit-code
 	} | test_copy_bytes 4096 >huge.tar &&
 	echo 141 >expect &&
 	test_cmp expect exit-code
diff --git a/t/t6002-rev-list-bisect.sh b/t/t6002-rev-list-bisect.sh
index daa009c9a1..f2de40b5ed 100755
--- a/t/t6002-rev-list-bisect.sh
+++ b/t/t6002-rev-list-bisect.sh
@@ -27,13 +27,16 @@ test_bisection_diff()
 	# Test if bisection size is close to half of list size within
 	# tolerance.
 	#
-	_bisect_err=$(expr $_list_size - $_bisection_size \* 2)
-	test "$_bisect_err" -lt 0 && _bisect_err=$(expr 0 - $_bisect_err)
-	_bisect_err=$(expr $_bisect_err / 2) ; # floor
+	_bisect_err=$(($_list_size - $_bisection_size * 2))
+	if test "$_bisect_err" -lt 0
+	then
+		_bisect_err=$((0 - $_bisect_err))
+	fi
+	_bisect_err=$(($_bisect_err / 2)) ; # floor
 
-	test_expect_success \
-	"bisection diff $_bisect_option $_head $* <= $_max_diff" \
-	'test $_bisect_err -le $_max_diff'
+	test_expect_success "bisection diff $_bisect_option $_head $* <= $_max_diff" '
+		test $_bisect_err -le $_max_diff
+	'
 }
 
 date >path0
diff --git a/t/t7422-submodule-output.sh b/t/t7422-submodule-output.sh
index aea1ddf117..852136fdfd 100755
--- a/t/t7422-submodule-output.sh
+++ b/t/t7422-submodule-output.sh
@@ -198,7 +198,7 @@ test_expect_success !MINGW 'git submodule status --recursive propagates SIGPIPE'
 	(
 		cd repo &&
 		GIT_ALLOW_PROTOCOL=file git submodule add "$(pwd)"/../submodule &&
-		{ git submodule status --recursive 2>err; echo $?>status; } |
+		{ { ret=0 && git submodule status --recursive 2>err || ret=$?; } && echo $ret >status; } |
 			grep -q recursive-submodule-path-1 &&
 		test_must_be_empty err &&
 		test_match_signal 13 "$(cat status)"
diff --git a/t/t7450-bad-git-dotfiles.sh b/t/t7450-bad-git-dotfiles.sh
index f512eed278..8cc86522b2 100755
--- a/t/t7450-bad-git-dotfiles.sh
+++ b/t/t7450-bad-git-dotfiles.sh
@@ -220,17 +220,19 @@ check_dotx_symlink () {
 		)
 	'
 
-	test -n "$refuse_index" &&
-	test_expect_success "refuse to load symlinked $name into index ($type)" '
-		test_must_fail \
-			git -C $dir \
-			    -c core.protectntfs \
-			    -c core.protecthfs \
-			    read-tree $tree 2>err &&
-		grep "invalid path.*$name" err &&
-		git -C $dir ls-files -s >out &&
-		test_must_be_empty out
-	'
+	if test -n "$refuse_index"
+	then
+		test_expect_success "refuse to load symlinked $name into index ($type)" '
+			test_must_fail \
+				git -C $dir \
+				    -c core.protectntfs \
+				    -c core.protecthfs \
+				    read-tree $tree 2>err &&
+			grep "invalid path.*$name" err &&
+			git -C $dir ls-files -s >out &&
+			test_must_be_empty out
+		'
+	fi
 }
 
 check_dotx_symlink gitmodules vanilla .gitmodules
diff --git a/t/t7508-status.sh b/t/t7508-status.sh
index a5e21bf8bf..1167b835a4 100755
--- a/t/t7508-status.sh
+++ b/t/t7508-status.sh
@@ -773,8 +773,8 @@ test_expect_success TTY 'status --porcelain ignores color.status' '
 '
 
 # recover unconditionally from color tests
-git config --unset color.status
-git config --unset color.ui
+git config --unset color.status || :
+git config --unset color.ui || :
 
 test_expect_success 'status --porcelain respects -b' '
 
diff --git a/t/t9138-git-svn-authors-prog.sh b/t/t9138-git-svn-authors-prog.sh
index 784ec7fc2d..5bb38cb23a 100755
--- a/t/t9138-git-svn-authors-prog.sh
+++ b/t/t9138-git-svn-authors-prog.sh
@@ -68,8 +68,8 @@ test_expect_success 'authors-file overrode authors-prog' '
 	)
 '
 
-git --git-dir=x/.git config --unset svn.authorsfile
-git --git-dir=x/.git config --unset svn.authorsprog
+git --git-dir=x/.git config --unset svn.authorsfile || :
+git --git-dir=x/.git config --unset svn.authorsprog || :
 
 test_expect_success 'authors-prog imported user without email' '
 	svn mkdir -m gg --username gg-hermit "$svnrepo"/gg &&
diff --git a/t/t9200-git-cvsexportcommit.sh b/t/t9200-git-cvsexportcommit.sh
index 14cbe96527..581cf3d28f 100755
--- a/t/t9200-git-cvsexportcommit.sh
+++ b/t/t9200-git-cvsexportcommit.sh
@@ -11,8 +11,7 @@ if ! test_have_prereq PERL; then
 	test_done
 fi
 
-cvs >/dev/null 2>&1
-if test $? -ne 1
+if ! cvs version >/dev/null 2>&1
 then
     skip_all='skipping git cvsexportcommit tests, cvs not found'
     test_done
diff --git a/t/t9400-git-cvsserver-server.sh b/t/t9400-git-cvsserver-server.sh
index e499c7f955..4b45398bab 100755
--- a/t/t9400-git-cvsserver-server.sh
+++ b/t/t9400-git-cvsserver-server.sh
@@ -17,12 +17,13 @@ if ! test_have_prereq PERL; then
 	skip_all='skipping git cvsserver tests, perl not available'
 	test_done
 fi
-cvs >/dev/null 2>&1
-if test $? -ne 1
+
+if ! cvs version >/dev/null 2>&1
 then
     skip_all='skipping git-cvsserver tests, cvs not found'
     test_done
 fi
+
 perl -e 'use DBI; use DBD::SQLite' >/dev/null 2>&1 || {
     skip_all='skipping git-cvsserver tests, Perl SQLite interface unavailable'
     test_done
diff --git a/t/t9401-git-cvsserver-crlf.sh b/t/t9401-git-cvsserver-crlf.sh
index a34805acdc..6b4cbb1651 100755
--- a/t/t9401-git-cvsserver-crlf.sh
+++ b/t/t9401-git-cvsserver-crlf.sh
@@ -60,12 +60,12 @@ check_status_options() {
     return $stat
 }
 
-cvs >/dev/null 2>&1
-if test $? -ne 1
+if ! cvs version >/dev/null 2>&1
 then
     skip_all='skipping git-cvsserver tests, cvs not found'
     test_done
 fi
+
 if ! test_have_prereq PERL
 then
     skip_all='skipping git-cvsserver tests, perl not available'
diff --git a/t/t9402-git-cvsserver-refs.sh b/t/t9402-git-cvsserver-refs.sh
index 2ee41f9443..65f2ceedec 100755
--- a/t/t9402-git-cvsserver-refs.sh
+++ b/t/t9402-git-cvsserver-refs.sh
@@ -68,12 +68,12 @@ check_diff() {
 
 #########
 
-cvs >/dev/null 2>&1
-if test $? -ne 1
+if ! cvs version >/dev/null 2>&1
 then
 	skip_all='skipping git-cvsserver tests, cvs not found'
 	test_done
 fi
+
 if ! test_have_prereq PERL
 then
 	skip_all='skipping git-cvsserver tests, perl not available'
diff --git a/t/t9902-completion.sh b/t/t9902-completion.sh
index 2f9a597ec7..28f61f08fb 100755
--- a/t/t9902-completion.sh
+++ b/t/t9902-completion.sh
@@ -590,12 +590,10 @@ test_expect_success '__gitcomp - doesnt fail because of invalid variable name' '
 	__gitcomp "$invalid_variable_name"
 '
 
-read -r -d "" refs <<-\EOF
-main
+refs='main
 maint
 next
-seen
-EOF
+seen'
 
 test_expect_success '__gitcomp_nl - trailing space' '
 	test_gitcomp_nl "m" "$refs" <<-EOF
diff --git a/t/test-lib-functions.sh b/t/test-lib-functions.sh
index f3af10fb7e..502bb0ddcb 100644
--- a/t/test-lib-functions.sh
+++ b/t/test-lib-functions.sh
@@ -1195,8 +1195,9 @@ test_must_fail () {
 		echo >&7 "test_must_fail: only 'git' is allowed: $*"
 		return 1
 	fi
-	"$@" 2>&7
-	exit_code=$?
+
+	exit_code=0; "$@" 2>&7 || exit_code=$?
+
 	if test $exit_code -eq 0 && ! list_contains "$_test_ok" success
 	then
 		echo >&4 "test_must_fail: command succeeded: $*"
@@ -1247,8 +1248,7 @@ test_might_fail () {
 test_expect_code () {
 	want_code=$1
 	shift
-	"$@" 2>&7
-	exit_code=$?
+	exit_code=0; "$@" 2>&7 || exit_code=$?
 	if test $exit_code = $want_code
 	then
 		return 0
@@ -1512,7 +1512,7 @@ test_when_finished () {
 	test "${BASH_SUBSHELL-0}" = 0 ||
 	BUG "test_when_finished does nothing in a subshell"
 	test_cleanup="{ $*
-		} && (exit \"\$eval_ret\"); eval_ret=\$?; $test_cleanup"
+		} || eval_ret=\$?; $test_cleanup"
 }
 
 # This function can be used to schedule some commands to be run
@@ -1540,7 +1540,7 @@ test_atexit () {
 	test "${BASH_SUBSHELL-0}" = 0 ||
 	BUG "test_atexit does nothing in a subshell"
 	test_atexit_cleanup="{ $*
-		} && (exit \"\$eval_ret\"); eval_ret=\$?; $test_atexit_cleanup"
+		} || eval_ret=\$?; $test_atexit_cleanup"
 }
 
 # Deprecated wrapper for "git init", use "git init" directly instead
diff --git a/t/test-lib.sh b/t/test-lib.sh
index 70fd3e9baf..cded7bd693 100644
--- a/t/test-lib.sh
+++ b/t/test-lib.sh
@@ -15,6 +15,31 @@
 # You should have received a copy of the GNU General Public License
 # along with this program.  If not, see https://www.gnu.org/licenses/ .
 
+# Enable the use of errexit so that any unexpected failures will cause us to
+# abort tests, even when outside of a specific test case.
+#
+# Note that we only enable this on Bash 5 and newer, or when explicitly
+# requested by the user via `GIT_TEST_USE_SET_E=true`. This ib secause `set -e`
+# has wildly different behaviour across shells. The list of default-enabled
+# shells may be extended going forward.
+if test -z "$GIT_TEST_USE_SET_E" && test "${BASH_VERSINFO:=0}" -ge 5
+then
+	GIT_TEST_USE_SET_E=true
+fi
+
+# We cannot use `test-tool env-helper` here, as it's not yet available.
+case "${GIT_TEST_USE_SET_E:-false}" in
+1|on|true|yes)
+	set -e
+	;;
+0|off|false|no)
+	;;
+*)
+	echo "GIT_TEST_USE_SET_E requires a boolean" >&2
+	exit 1
+	;;
+esac
+
 # Test the binaries we have just built.  The tests are kept in
 # t/ subdirectory and are run in 'trash directory' subdirectory.
 if test -z "$TEST_DIRECTORY"
@@ -143,8 +168,8 @@ export GIT_TEST_DEFAULT_INITIAL_BRANCH_NAME
 ################################################################
 # It appears that people try to run tests without building...
 GIT_BINARY="${GIT_TEST_INSTALLED:-$GIT_BUILD_DIR}/git$X"
-"$GIT_BINARY" >/dev/null
-if test $? != 1
+
+if ! "$GIT_BINARY" version >/dev/null
 then
 	if test -n "$GIT_TEST_INSTALLED"
 	then
@@ -454,8 +479,10 @@ then
 	# from any previous runs.
 	>"$GIT_TEST_TEE_OUTPUT_FILE"
 
-	(GIT_TEST_TEE_STARTED=done ${TEST_SHELL_PATH} "$0" "$@" 2>&1;
-	 echo $? >"$TEST_RESULTS_BASE.exit") | tee -a "$GIT_TEST_TEE_OUTPUT_FILE"
+	(
+		ret=0 && GIT_TEST_TEE_STARTED=done ${TEST_SHELL_PATH} "$0" "$@" 2>&1 || ret=$?
+		echo "$ret" >"$TEST_RESULTS_BASE.exit"
+	) | tee -a "$GIT_TEST_TEE_OUTPUT_FILE"
 	test "$(cat "$TEST_RESULTS_BASE.exit")" = 0
 	exit
 fi