diff --git a/Makeconfig b/Makeconfig
index 8fe7217dd7..6cd590cf21 100644
--- a/Makeconfig
+++ b/Makeconfig
@@ -782,6 +782,14 @@ run-built-tests = yes
 endif
 endif
 
+# Whether the timing-sensitive test runs are serialized: each is run with
+# .NOTPARALLEL and, at the top level, ordered after the rest of the test run.
+# This is the default; 'make check-parallel' clears it to run every test
+# concurrently.
+ifndef serialize-tests
+serialize-tests = yes
+endif
+
 # Whether to build the static math tests
 ifndef build-math-static-tests
 build-math-static-tests = no
diff --git a/Makefile b/Makefile
index b421dbbafb..54de425e9e 100644
--- a/Makefile
+++ b/Makefile
@@ -594,7 +594,9 @@ $(objpfx)testroot.pristine/install.stamp: | others
 # 'make subdir/tests' is left alone.  And it only orders the test run
 # (run-built-tests=yes); the "build the tests" pass (run-built-tests=no)
 # is left fully parallel, so every test program still builds concurrently.
+# serialize-tests=no ('make check-parallel') drops the ordering entirely.
 ifeq ($(run-built-tests),yes)
+ifeq (yes,$(serialize-tests))
 ifneq (,$(filter tests xtests check xcheck,$(MAKECMDGOALS)))
 +late-test-subdirs := $(filter nptl htl,$(subdirs)) $(filter rt,$(subdirs))
 +test-run-prev := \
@@ -604,6 +606,7 @@ $(foreach d,$(+late-test-subdirs),\
   $(eval +test-run-prev += $(d)/tests))
 endif
 endif
+endif
 
 ifeq (yes,$(build-shared))
 # The top-level libc.so and linkobj/libc_pic.a rules list these
diff --git a/Makerules b/Makerules
index 38a01d38be..6bef57ece9 100644
--- a/Makerules
+++ b/Makerules
@@ -1214,6 +1214,19 @@ check: tests
 xcheck: xtests
 endif
 
+# 'make check-parallel' runs the whole suite with maximum concurrency:
+# serialize-tests=no drops the per-subdirectory .NOTPARALLEL and the run-time
+# ordering, so every test builds and runs in parallel.  A single pass suffices
+# (there is no .NOTPARALLEL to work around, so the test programs already build
+# concurrently).
+# This is faster on an idle machine, at the cost of possible flakiness in the
+# timing-sensitive tests under the heavier load.
+.PHONY: check-parallel xcheck-parallel
+check-parallel:
+	$(MAKE) serialize-tests=no tests
+xcheck-parallel:
+	$(MAKE) serialize-tests=no xtests
+
 # Also handle test inputs in sysdeps.
 vpath %.input $(sysdirs)
 
diff --git a/htl/Makefile b/htl/Makefile
index 31e8ffd8e1..8078a7ade1 100644
--- a/htl/Makefile
+++ b/htl/Makefile
@@ -259,7 +259,7 @@ $(addprefix $(objpfx),$(tests) $(test-srcs)): $(srcdir)/libpthread_syms.a $(objp
 endif
 
 # Like rt, these tests prefer to be run serially.
-ifeq ($(run-built-tests),yes)
+ifeq (yes-yes,$(run-built-tests)-$(serialize-tests))
 ifneq ($(filter %tests,$(MAKECMDGOALS)),)
 .NOTPARALLEL:
 endif
diff --git a/nptl/Makefile b/nptl/Makefile
index 02862d1c04..97a0fb7f65 100644
--- a/nptl/Makefile
+++ b/nptl/Makefile
@@ -738,8 +738,9 @@ tst-audit-threads-ENV = LD_AUDIT=$(objpfx)tst-audit-threads-mod1.so
 tst-setuid1-static-ENV = \
   LD_LIBRARY_PATH=$(ld-library-path):$(common-objpfx)elf:$(common-objpfx)nss
 
-# The tests here better do not run in parallel.
-ifeq ($(run-built-tests),yes)
+# The tests here better do not run in parallel, unless serialize-tests is
+# cleared (make check-parallel).
+ifeq (yes-yes,$(run-built-tests)-$(serialize-tests))
 ifneq ($(filter %tests,$(MAKECMDGOALS)),)
 .NOTPARALLEL:
 endif
diff --git a/rt/Makefile b/rt/Makefile
index 24e43a8759..f39e9674e5 100644
--- a/rt/Makefile
+++ b/rt/Makefile
@@ -111,8 +111,9 @@ $(objpfx)librt.so: $(shared-thread-library)
 tst-mqueue7-ARGS = -- $(host-test-program-cmd)
 
 # The timer and message-queue tests here are timing-sensitive and better
-# do not run in parallel.
-ifeq ($(run-built-tests),yes)
+# do not run in parallel, unless serialize-tests is cleared (make
+# check-parallel).
+ifeq (yes-yes,$(run-built-tests)-$(serialize-tests))
 ifneq ($(filter %tests,$(MAKECMDGOALS)),)
 .NOTPARALLEL:
 endif