diff --git a/src/backend/postmaster/pgstat.c b/src/backend/postmaster/pgstat.c
index b5ce2f6cc7..d251fddc0b 100644
--- a/src/backend/postmaster/pgstat.c
+++ b/src/backend/postmaster/pgstat.c
@@ -329,6 +329,16 @@ pgstat_init(void)
 
 #define TESTBYTEVAL ((char) 199)
 
+	/*
+	 * This static assertion verifies that we didn't mess up the calculations
+	 * involved in selecting maximum payload sizes for our UDP messages.
+	 * Because the only consequence of overrunning PGSTAT_MAX_MSG_SIZE would
+	 * be silent performance loss from fragmentation, it seems worth having a
+	 * compile-time cross-check that we didn't.
+	 */
+	StaticAssertStmt(sizeof(PgStat_Msg) <= PGSTAT_MAX_MSG_SIZE,
+				   'maximum stats message size exceeds PGSTAT_MAX_MSG_SIZE');
+
 	/*
 	 * Create the UDP socket for sending and receiving statistic messages
 	 */
diff --git a/src/include/pgstat.h b/src/include/pgstat.h
index fb242e4b91..b79a0ebcc3 100644
--- a/src/include/pgstat.h
+++ b/src/include/pgstat.h
@@ -177,11 +177,13 @@ typedef struct PgStat_MsgHdr
 
 /* ----------
  * Space available in a message.  This will keep the UDP packets below 1K,
- * which should fit unfragmented into the MTU of the lo interface on most
- * platforms. Does anybody care for platforms where it doesn't?
+ * which should fit unfragmented into the MTU of the loopback interface.
+ * (Larger values of PGSTAT_MAX_MSG_SIZE would work for that on most
+ * platforms, but we're being conservative here.)
  * ----------
  */
-#define PGSTAT_MSG_PAYLOAD	(1000 - sizeof(PgStat_MsgHdr))
+#define PGSTAT_MAX_MSG_SIZE 1000
+#define PGSTAT_MSG_PAYLOAD	(PGSTAT_MAX_MSG_SIZE - sizeof(PgStat_MsgHdr))
 
 
 /* ----------
@@ -225,7 +227,7 @@ typedef struct PgStat_TableEntry
  * ----------
  */
 #define PGSTAT_NUM_TABENTRIES  \
-	((PGSTAT_MSG_PAYLOAD - sizeof(Oid) - 3 * sizeof(int))  \
+	((PGSTAT_MSG_PAYLOAD - sizeof(Oid) - 3 * sizeof(int) - 2 * sizeof(PgStat_Counter))	\
 	 / sizeof(PgStat_TableEntry))
 
 typedef struct PgStat_MsgTabstat