diff --git a/doc/src/sgml/runtime.sgml b/doc/src/sgml/runtime.sgml
index 94135e9d5ee..8750044852d 100644
--- a/doc/src/sgml/runtime.sgml
+++ b/doc/src/sgml/runtime.sgml
@@ -782,19 +782,19 @@ psql: error: connection to server on socket "/tmp/.s.PGSQL.5432" failed: No such
        <row>
         <entry><varname>SEMMNI</varname></entry>
         <entry>Maximum number of semaphore identifiers (i.e., sets)</entry>
-        <entry>at least <literal>ceil(num_os_semaphores / 16)</literal> plus room for other applications</entry>
+        <entry>at least <literal>ceil(num_os_semaphores / 19)</literal> plus room for other applications</entry>
        </row>
 
        <row>
         <entry><varname>SEMMNS</varname></entry>
         <entry>Maximum number of semaphores system-wide</entry>
-        <entry><literal>ceil(num_os_semaphores / 16) * 17</literal> plus room for other applications</entry>
+        <entry><literal>ceil(num_os_semaphores / 19) * 20</literal> plus room for other applications</entry>
        </row>
 
        <row>
         <entry><varname>SEMMSL</varname></entry>
         <entry>Maximum number of semaphores per set</entry>
-        <entry>at least 17</entry>
+        <entry>at least 20</entry>
        </row>
 
        <row>
@@ -841,7 +841,7 @@ psql: error: connection to server on socket "/tmp/.s.PGSQL.5432" failed: No such
     (<xref linkend="guc-max-connections"/>), allowed autovacuum worker process
     (<xref linkend="guc-autovacuum-max-workers"/>), allowed WAL sender process
     (<xref linkend="guc-max-wal-senders"/>), allowed background
-    process (<xref linkend="guc-max-worker-processes"/>), etc., in sets of 16.
+    process (<xref linkend="guc-max-worker-processes"/>), etc., in sets of 19.
     The runtime-computed parameter <xref linkend="guc-num-os-semaphores"/>
     reports the number of semaphores required.  This parameter can be viewed
     before starting the server with a <command>postgres</command> command like:
@@ -851,17 +851,17 @@ $ <userinput>postgres -D $PGDATA -C num_os_semaphores</userinput>
    </para>
 
    <para>
-    Each set of 16 semaphores will
-    also contain a 17th semaphore which contains a <quote>magic
+    Each set of 19 semaphores will
+    also contain a 20th semaphore which contains a <quote>magic
     number</quote>, to detect collision with semaphore sets used by
     other applications. The maximum number of semaphores in the system
     is set by <varname>SEMMNS</varname>, which consequently must be at least
     as high as <literal>num_os_semaphores</literal> plus one extra for
-    each set of 16 required semaphores (see the formula in <xref
+    each set of 19 required semaphores (see the formula in <xref
     linkend="sysvipc-parameters"/>).  The parameter <varname>SEMMNI</varname>
     determines the limit on the number of semaphore sets that can
     exist on the system at one time.  Hence this parameter must be at
-    least <literal>ceil(num_os_semaphores / 16)</literal>.
+    least <literal>ceil(num_os_semaphores / 19)</literal>.
     Lowering the number
     of allowed connections is a temporary workaround for failures,
     which are usually confusingly worded <quote>No space
diff --git a/src/backend/port/sysv_sema.c b/src/backend/port/sysv_sema.c
index 5b88a92bc95..68835723b90 100644
--- a/src/backend/port/sysv_sema.c
+++ b/src/backend/port/sysv_sema.c
@@ -50,8 +50,14 @@ typedef int IpcSemaphoreId;		/* semaphore ID returned by semget(2) */
  * we allocate.  It must be *less than* your kernel's SEMMSL (max semaphores
  * per set) parameter, which is often around 25.  (Less than, because we
  * allocate one extra sema in each set for identification purposes.)
+ *
+ * The present value of 19 is chosen with one eye on NetBSD/OpenBSD's default
+ * SEMMNS setting of 60.  Remembering the extra sema per set, this lets us
+ * allocate three sets with 57 useful semaphores before exceeding that, which
+ * is enough to run our core regression tests.  Users of those systems will
+ * still want to raise SEMMNS for any sort of production work, though.
  */
-#define SEMAS_PER_SET	16
+#define SEMAS_PER_SET	19
 
 #define IPCProtection	(0600)	/* access/modify by user only */
 
diff --git a/src/bin/initdb/initdb.c b/src/bin/initdb/initdb.c
index 9a91830783e..49e8efd2125 100644
--- a/src/bin/initdb/initdb.c
+++ b/src/bin/initdb/initdb.c
@@ -1119,7 +1119,7 @@ test_config_settings(void)
 #define MIN_BUFS_FOR_CONNS(nconns)	((nconns) * 10)
 
 	static const int trial_conns[] = {
-		100, 50, 40, 30, 20
+		100, 50, 40, 30, 25
 	};
 	static const int trial_bufs[] = {
 		16384, 8192, 4096, 3584, 3072, 2560, 2048, 1536,