diff --git a/Makefile b/Makefile
index 27375f0..0b8079c 100644
--- a/Makefile
+++ b/Makefile
@@ -521,8 +521,8 @@
 
 no-dot-config-targets := clean clobber mrproper distclean \
 			 help %docs check% coccicheck \
-			 ubootversion backup tests check qcheck tcheck pylint \
-			 pylint_err
+			 ubootversion backup tests check pcheck qcheck tcheck \
+			 pylint pylint_err
 
 config-targets := 0
 mixed-targets  := 0
@@ -2364,6 +2364,7 @@
 	@echo  'Test targets:'
 	@echo  ''
 	@echo  '  check           - Run all automated tests that use sandbox'
+	@echo  '  pcheck          - Run quick automated tests in parallel'
 	@echo  '  qcheck          - Run quick automated tests that use sandbox'
 	@echo  '  tcheck          - Run quick automated tests on tools'
 	@echo  '  pylint          - Run pylint on all Python files'
@@ -2409,6 +2410,9 @@
 tests check:
 	$(srctree)/test/run
 
+pcheck:
+	$(srctree)/test/run parallel
+
 qcheck:
 	$(srctree)/test/run quick
 
diff --git a/doc/develop/py_testing.rst b/doc/develop/py_testing.rst
index 06f9196..92fbd22 100644
--- a/doc/develop/py_testing.rst
+++ b/doc/develop/py_testing.rst
@@ -121,31 +121,36 @@
 Running tests in parallel
 ~~~~~~~~~~~~~~~~~~~~~~~~~
 
-Note: This does not fully work yet and is documented only so you can try to
-fix the problems.
+Note: Not all tests can run in parallel at present, so the usual approach is
+to just run those that can.
 
 First install support for parallel tests::
 
+    sudo apt install python3-pytest-xdist
+
+or:::
+
     pip3 install pytest-xdist
 
-Then build sandbox in a suitable build directory. It is not possible to use
-the --build flag with xdist.
+Then run the tests in parallel using the -n flag::
 
-Finally, run the tests in parallel using the -n flag::
+    test/py/test.py -B sandbox --build --build-dir /tmp/b/sandbox -q -k \
+        'not slow and not bootstd and not spi_flash' -n16
 
-    # build sandbox first, in a suitable build directory. It is not possible
-    # to use the --build flag with -n
-    test/py/test.py -B sandbox --build-dir /tmp/b/sandbox -q -k 'not slow' -n32
+You can also use `make pcheck` to run all tests in parallel. This uses a maximum
+of 16 threads, since the setup time is significant and there are under 1000
+tests.
 
-At least the following non-slow tests are known to fail:
+Note that the `test-log.html` output does not work correctly at present with
+parallel testing. All the threads write to it at once, so it is garbled.
 
-- test_fit_ecdsa
-- test_bind_unbind_with_uclass
-- ut_dm_spi_flash
-- test_gpt_rename_partition
-- test_gpt_swap_partitions
-- test_pinmux_status
-- test_sqfs_load
+Note that the `tools/` tests still run each tool's tests once after the other,
+although within that, they do run in parallel. So for example, the buildman
+tests run in parallel, then the binman tests run in parallel. There would be a
+significant advantage to running them all in parallel together, but that would
+require a large amount of refactoring, e.g. with more use of pytest fixtures.
+The code-coverage tests are omitted since they cannot run in parallel due to a
+Python limitation.
 
 
 Testing under a debugger
diff --git a/doc/develop/testing.rst b/doc/develop/testing.rst
index 1abe4d7..5afeb42 100644
--- a/doc/develop/testing.rst
+++ b/doc/develop/testing.rst
@@ -28,8 +28,12 @@
 
     make tcheck
 
+You can also run a selection tests in parallel with::
+
+    make pcheck
+
 All of the above use the test/run script with a paremeter to select which tests
-are run.
+are run. See :doc:`py_testing` for more information.
 
 
 Sandbox
diff --git a/test/run b/test/run
index 0c8aeb5..810b47e 100755
--- a/test/run
+++ b/test/run
@@ -14,27 +14,46 @@
 }
 
 # Select test attributes
+ut_mark_expr=test_ut
 if [ "$1" = "quick" ]; then
 	mark_expr="not slow"
+	ut_mark_expr="test_ut and not slow"
 	skip=--skip-net-tests
 fi
 
 [ "$1" == "tools" ] && tools_only=y
 
+if [ "$1" = "parallel" ]; then
+	if ! echo 'import xdist' | python3 2>/dev/null; then
+		echo "Please install python3-pytest-xdist - see doc/develop/py_testing.rst"
+		exit 1
+	fi
+	jobs="$(($(nproc) > 16 ? 16 : $(nproc)))"
+	para="-n${jobs} -q"
+	prompt="Building and..."
+	skip=--skip-net-tests
+	mark_expr="not slow and not bootstd and not spi_flash"
+	ut_mark_expr="test_ut and not slow and not bootstd and not spi_flash"
+	echo "Note: test log is garbled with parallel tests"
+fi
+
 failures=0
 
 if [ -z "$tools_only" ]; then
 	# Run all tests that the standard sandbox build can support
-	run_test "sandbox" ./test/py/test.py --bd sandbox --build \
+	echo "${prompt}"
+	run_test "sandbox" ./test/py/test.py --bd sandbox --build ${para} \
 		-k "${mark_expr}"
 fi
 
 # Run tests which require sandbox_spl
-run_test "sandbox_spl" ./test/py/test.py --bd sandbox_spl --build \
+echo "${prompt}"
+run_test "sandbox_spl" ./test/py/test.py --bd sandbox_spl --build ${para} \
 		-k 'test_ofplatdata or test_handoff or test_spl'
 
 # Run the sane tests with sandbox_noinst (i.e. without OF_PLATDATA_INST)
-run_test "sandbox_spl" ./test/py/test.py --bd sandbox_noinst --build \
+echo "${prompt}"
+run_test "sandbox_spl" ./test/py/test.py --bd sandbox_noinst --build ${para} \
 		-k 'test_ofplatdata or test_handoff or test_spl'
 
 if [ -z "$tools_only" ]; then
@@ -42,8 +61,9 @@
 	# build which does not enable CONFIG_OF_LIVE for the live device tree, so we can
 	# check that functionality is the same. The standard sandbox build (above) uses
 	# CONFIG_OF_LIVE.
+	echo "${prompt}"
 	run_test "sandbox_flattree" ./test/py/test.py --bd sandbox_flattree \
-		--build -k test_ut
+		${para} --build -k "${ut_mark_expr}"
 fi
 
 # Set up a path to dtc (device-tree compiler) and libfdt.py, a library it
@@ -64,10 +84,14 @@
 # This needs you to set up Python test coverage tools.
 # To enable Python test coverage on Debian-type distributions (e.g. Ubuntu):
 #   $ sudo apt-get install python-pytest python-coverage
-export PATH=$PATH:${TOOLS_DIR}
-run_test "binman code coverage" ./tools/binman/binman test -T
-run_test "dtoc code coverage" ./tools/dtoc/dtoc -T
-run_test "fdt code coverage" ./tools/dtoc/test_fdt -T
+
+# Code-coverage tests cannot run in parallel, so skip them in that case
+if [ -z "${para}" ]; then
+	export PATH=$PATH:${TOOLS_DIR}
+	run_test "binman code coverage" ./tools/binman/binman test -T
+	run_test "dtoc code coverage" ./tools/dtoc/dtoc -T
+	run_test "fdt code coverage" ./tools/dtoc/test_fdt -T
+fi
 
 if [ $failures == 0 ]; then
 	echo "Tests passed!"