diff --git a/doc/src/sgml/ref/psql-ref.sgml b/doc/src/sgml/ref/psql-ref.sgml
index 4b5e5274e5..0675a8e17b 100644
--- a/doc/src/sgml/ref/psql-ref.sgml
+++ b/doc/src/sgml/ref/psql-ref.sgml
@@ -3505,14 +3505,24 @@ PSQL_EDITOR_LINENUMBER_ARG='--line '
       </listitem>
 
       <listitem>
-      <para><application>psql</application> is only guaranteed to work smoothly
-       with servers of the same version. That does not mean other combinations
-       will fail outright, but subtle and not-so-subtle problems might come
-       up.  Backslash commands are particularly likely to fail if the
-       server is of a newer version than <application>psql</> itself.  However,
-       backslash commands of the <literal>\d</> family should work with
-       servers of versions back to 7.4, though not necessarily with servers
-       newer than  <application>psql</> itself.
+      <para><application>psql</application> works best with servers of the same
+       or an older major version.  Backslash commands are particularly likely
+       to fail if the server is of a newer version than <application>psql</>
+       itself.  However, backslash commands of the <literal>\d</> family should
+       work with servers of versions back to 7.4, though not necessarily with
+       servers newer than <application>psql</> itself.  The general
+       functionality of running SQL commands and displaying query results
+       should also work with servers of a newer major version, but this cannot
+       be guaranteed in all cases.
+      </para>
+      <para>
+       If you want to use <application>psql</application> to connect to several
+       servers of different major versions, it is recommended that you use the
+       newest version of <application>psql</application>.  Alternatively, you
+       can keep a copy of <application>psql</application> from each major
+       version around and be sure to use the version that matches the
+       respective server.  But in practice, this additional complication should
+       not be necessary.
       </para>
       </listitem>
 
diff --git a/src/bin/psql/command.c b/src/bin/psql/command.c
index dc04399d0b..b90d2f12b9 100644
--- a/src/bin/psql/command.c
+++ b/src/bin/psql/command.c
@@ -1694,8 +1694,8 @@ connection_warnings(bool in_startup)
 		else if (in_startup)
 			printf("%s (%s)\n", pset.progname, PG_VERSION);
 
-		if (pset.sversion / 100 != client_ver / 100)
-			printf(_("WARNING: %s version %d.%d, server version %d.%d.\n"
+		if (pset.sversion / 100 > client_ver / 100)
+			printf(_("WARNING: %s major version %d.%d, server major version %d.%d.\n"
 					 "         Some psql features might not work.\n"),
 				 pset.progname, client_ver / 10000, (client_ver / 100) % 100,
 				   pset.sversion / 10000, (pset.sversion / 100) % 100);