diff --git a/test/Makefile.in b/test/Makefile.in
index 0d26303a637..21f31f4c2d0 100644
--- a/test/Makefile.in
+++ b/test/Makefile.in
@@ -219,8 +219,13 @@ LOGFILES := $(patsubst %.el,%.log, \
 TESTS := $(LOGFILES:.log=)
 
 ## Some tests show problems when run in parallel with other tests.
-## Suppress parallelism for them.
-.NOTPARALLEL: lisp/filenotify-tests.log lisp/net/tramp-tests.log
+## Suppress parallelism for them when SELECTOR is equal to
+## SELECTOR_EXPENSIVE or SELECTOR_ALL.
+PARALLEL_TESTS := $(LOGFILES)
+ifeq ($(subst $(SELECTOR_ALL),yes,$(subst $(SELECTOR_EXPENSIVE),yes,$(SELECTOR_ACTUAL))), yes)
+$(eval NOT_PARALLEL_TESTS := $(filter lisp/autorevert-tests.log lisp/filenotify-tests.log lisp/net/tramp-tests.log, $(LOGFILES)))
+$(eval PARALLEL_TESTS := $(filter-out $(NOT_PARALLEL_TESTS), ${LOGFILES}))
+endif
 
 ## If we have to interrupt a hanging test, preserve the log so we can
 ## see what the problem was.
@@ -352,7 +357,12 @@ ifeq ($(TEST_INTERACTIVE), yes)
 	  $(patsubst %,-l %,$(if $(findstring $(TEST_LOAD_EL),yes),$ELFILES,$(ELFILES:.el=))) \
 	  $(TEST_RUN_ERT)
 else
-	-@${MAKE} -k ${LOGFILES}
+ifdef NOT_PARALLEL_TESTS
+	-@${MAKE} -k -j1 ${NOT_PARALLEL_TESTS}
+endif
+ifdef PARALLEL_TESTS
+	-@${MAKE} -k ${PARALLEL_TESTS}
+endif
 	@$(emacs) --batch -l ert --eval \
 	"(ert-summarize-tests-batch-and-exit ${SUMMARIZE_TESTS})" ${LOGFILES}
 endif
diff --git a/test/README b/test/README
index a287ae69734..fa48b690347 100644
--- a/test/README
+++ b/test/README
@@ -35,7 +35,9 @@ test" instead.
 
 Running several tests in parallel could result in unexpected side
 effects with ephemeral test errors.  Therefore, it is recommend not to
-use "make -j".
+use "make -j".  Nonetheless, when expensive tests are activated, some of
+the tests do not run parallel anyway.  See make variable
+$NOT_PARALLEL_TESTS.
 
 The Makefile sets the environment variable $EMACS_TEST_DIRECTORY,
 which points to this directory.  This environment variable does not
@@ -97,6 +99,9 @@ use it directly:
 
     make <filename> SELECTOR='test-foo-remote'
 
+Setting $SELECTOR in combination with the check-expensive or check-all
+make targets is ignored.
+
 Note that although the test files are always compiled (unless they set
 no-byte-compile), the source files will be run when expensive or
 unstable tests are involved, to give nicer backtraces.  To run the
diff --git a/test/infra/gitlab-ci.yml b/test/infra/gitlab-ci.yml
index 23af677d186..1f0f33bbe86 100644
--- a/test/infra/gitlab-ci.yml
+++ b/test/infra/gitlab-ci.yml
@@ -90,6 +90,7 @@ default:
      -e EMACS_TEST_JUNIT_REPORT=${EMACS_TEST_JUNIT_REPORT}
      -e EMACS_TEST_TIMEOUT=${EMACS_TEST_TIMEOUT}
      -e EMACS_TEST_VERBOSE=${EMACS_TEST_VERBOSE}
+     -e NPROC=`nproc`
      -e http_proxy=${http_proxy}
      -e https_proxy=${https_proxy}
      -e no_proxy=${no_proxy}
@@ -103,8 +104,8 @@ default:
         git diff --name-only FETCH_HEAD &&
         ( git diff --name-only FETCH_HEAD |
           xargs git checkout -f FETCH_HEAD ) &&
-        make &&
-        make -k ${make_params}"'
+        make -j \$NPROC &&
+        make -k -j \$NPROC ${make_params}"'
   after_script:
     # - docker ps -a
     # - pwd; printenv