diff --git a/src/backend/libpq/be-secure.c b/src/backend/libpq/be-secure.c
index d1beda871f8..b391af34fb9 100644
--- a/src/backend/libpq/be-secure.c
+++ b/src/backend/libpq/be-secure.c
@@ -887,7 +887,6 @@ open_server_SSL(Port *port)
 				(errcode(ERRCODE_PROTOCOL_VIOLATION),
 				 errmsg("could not initialize SSL connection: %s",
 						SSLerrmessage())));
-		close_SSL(port);
 		return -1;
 	}
 	if (!my_SSL_set_fd(port->ssl, port->sock))
@@ -896,7 +895,6 @@ open_server_SSL(Port *port)
 				(errcode(ERRCODE_PROTOCOL_VIOLATION),
 				 errmsg("could not set SSL socket: %s",
 						SSLerrmessage())));
-		close_SSL(port);
 		return -1;
 	}
 
@@ -944,7 +942,6 @@ aloop:
 								err)));
 				break;
 		}
-		close_SSL(port);
 		return -1;
 	}
 
@@ -973,7 +970,6 @@ aloop:
 			{
 				/* shouldn't happen */
 				pfree(peer_cn);
-				close_SSL(port);
 				return -1;
 			}
 
@@ -987,7 +983,6 @@ aloop:
 						(errcode(ERRCODE_PROTOCOL_VIOLATION),
 						 errmsg("SSL certificate's common name contains embedded null")));
 				pfree(peer_cn);
-				close_SSL(port);
 				return -1;
 			}
 
diff --git a/src/backend/libpq/pqcomm.c b/src/backend/libpq/pqcomm.c
index c5404b414a8..b27a474dd7e 100644
--- a/src/backend/libpq/pqcomm.c
+++ b/src/backend/libpq/pqcomm.c
@@ -182,32 +182,45 @@ pq_comm_reset(void)
 /* --------------------------------
  *		pq_close - shutdown libpq at backend exit
  *
- * Note: in a standalone backend MyProcPort will be null,
- * don't crash during exit...
+ * This is the one pg_on_exit_callback in place during BackendInitialize().
+ * That function's unusual signal handling constrains that this callback be
+ * safe to run at any instant.
  * --------------------------------
  */
 static void
 pq_close(int code, Datum arg)
 {
+	/* Nothing to do in a standalone backend, where MyProcPort is NULL. */
 	if (MyProcPort != NULL)
 	{
 #if defined(ENABLE_GSS) || defined(ENABLE_SSPI)
 #ifdef ENABLE_GSS
 		OM_uint32	min_s;
 
-		/* Shutdown GSSAPI layer */
+		/*
+		 * Shutdown GSSAPI layer.  This section does nothing when interrupting
+		 * BackendInitialize(), because pg_GSS_recvauth() makes first use of
+		 * "ctx" and "cred".
+		 */
 		if (MyProcPort->gss->ctx != GSS_C_NO_CONTEXT)
 			gss_delete_sec_context(&min_s, &MyProcPort->gss->ctx, NULL);
 
 		if (MyProcPort->gss->cred != GSS_C_NO_CREDENTIAL)
 			gss_release_cred(&min_s, &MyProcPort->gss->cred);
 #endif   /* ENABLE_GSS */
-		/* GSS and SSPI share the port->gss struct */
 
+		/*
+		 * GSS and SSPI share the port->gss struct.  Since nowhere else does a
+		 * postmaster child free this, doing so is safe when interrupting
+		 * BackendInitialize().
+		 */
 		free(MyProcPort->gss);
 #endif   /* ENABLE_GSS || ENABLE_SSPI */
 
-		/* Cleanly shut down SSL layer */
+		/*
+		 * Cleanly shut down SSL layer.  Nowhere else does a postmaster child
+		 * call this, so this is safe when interrupting BackendInitialize().
+		 */
 		secure_close(MyProcPort);
 
 		/*
diff --git a/src/backend/postmaster/postmaster.c b/src/backend/postmaster/postmaster.c
index 84ba3aa0c0e..1965c863a8c 100644
--- a/src/backend/postmaster/postmaster.c
+++ b/src/backend/postmaster/postmaster.c
@@ -3855,7 +3855,16 @@ BackendInitialize(Port *port)
 	 * We arrange for a simple exit(1) if we receive SIGTERM or SIGQUIT or
 	 * timeout while trying to collect the startup packet.  Otherwise the
 	 * postmaster cannot shutdown the database FAST or IMMED cleanly if a
-	 * buggy client fails to send the packet promptly.
+	 * buggy client fails to send the packet promptly.  XXX it follows that
+	 * the remainder of this function must tolerate losing control at any
+	 * instant.  Likewise, any pg_on_exit_callback registered before or during
+	 * this function must be prepared to execute at any instant between here
+	 * and the end of this function.  Furthermore, affected callbacks execute
+	 * partially or not at all when a second exit-inducing signal arrives
+	 * after proc_exit_prepare() decrements on_proc_exit_index.  (Thanks to
+	 * that mechanic, callbacks need not anticipate more than one call.)  This
+	 * is fragile; it ought to instead follow the norm of handling interrupts
+	 * at selected, safe opportunities.
 	 */
 	pqsignal(SIGTERM, startup_die);
 	pqsignal(SIGQUIT, startup_die);