1 files changed, 10 insertions, 9 deletions
diff --git a/doc/automake.texi b/doc/automake.texi
index 239f9ef3f..a32d8bdc7 100644
--- a/doc/automake.texi
+++ b/doc/automake.texi
@@ -319,7 +319,7 @@ Support for test suites
 Simple Tests
 
 * Scripts-based Testsuites::    Automake-specific concepts and terminology
-* Serial Test Harness::         Older (and obsolescent) serial test harness
+* Serial Test Harness::         Older (and discouraged) serial test harness
 * Parallel Test Harness::       Generic concurrent test harness
 
 Using the TAP test protocol
@@ -8818,7 +8818,7 @@ terminology)?
 
 @menu
 * Scripts-based Testsuites::    Automake-specific concepts and terminology
-* Serial Test Harness::         Older (and obsolescent) serial test harness
+* Serial Test Harness::         Older (and discouraged) serial test harness
 * Parallel Test Harness::       Generic concurrent test harness
 @end menu
 
@@ -8991,12 +8991,16 @@ by the tests, not the tests themselves.  Of course you can set
 @code{TESTS = $(check_PROGRAMS)} if all your programs are test cases.
 
 @node Serial Test Harness
-@subsection Older (and obsolescent) serial test harness
+@subsection Older (and discouraged) serial test harness
 @cindex @option{serial-tests}, Using
 
-@emph{This harness is obsolescent}, and kept for backward-compatibility
-reasons only.  The user is strongly advised to just use the parallel test
-harness instead (@pxref{Parallel Test Harness}).
+First, note that today the use of this harness is strongly discouraged in
+favour of the parallel test harness (@pxref{Parallel Test Harness}).
+Still, there are @emph{few} situations when the advantages offered by
+the parallel harness are irrelevant, and when test concurrency can
+even cause tricky problems.  In those cases, it might make sense to
+still use the serial harness, for simplicity and reliability (we still
+suggest trying to give the parallel harness a shot though).
 
 The serial test harness is enabled by the Automake option
 @option{serial-tests}. It operates by simply running the tests serially,
@@ -9038,9 +9042,6 @@ files, concurrent execution of tests with @code{make -j}, specification
 of inter-test dependencies, lazy reruns of tests that have not completed
 in a prior run, and hard errors for exceptional failures.
 
-This harness is still somewhat experimental and may undergo changes in
-order to satisfy additional portability requirements.
-
 @anchor{Basics of test metadata}
 @vindex TEST_SUITE_LOG
 @vindex TESTS