diff --git a/ntp_core.c b/ntp_core.c
index 18e6684..6d5b857 100644
--- a/ntp_core.c
+++ b/ntp_core.c
@@ -899,8 +899,10 @@ transmit_packet(NTP_Mode my_mode, /* The mode this machine wants to be */
                 NTP_Local_Timestamp *local_rx, /* The RX time of the received packet */
                 NTP_Local_Timestamp *local_tx, /* The TX time of the previous packet
                                                   RESULT : TX time of this packet */
-                NTP_int64 *local_ntp_rx, /* RESULT : receive timestamp from this packet */
-                NTP_int64 *local_ntp_tx, /* RESULT : transmit timestamp from this packet */
+                NTP_int64 *local_ntp_rx, /* The receive timestamp from the previous packet
+                                            RESULT : receive timestamp from this packet */
+                NTP_int64 *local_ntp_tx, /* The transmit timestamp from the previous packet
+                                            RESULT : transmit timestamp from this packet */
                 NTP_Remote_Address *where_to, /* Where to address the reponse to */
                 NTP_Local_Address *from /* From what address to send it */
                 )
@@ -998,14 +1000,21 @@ transmit_packet(NTP_Mode my_mode, /* The mode this machine wants to be */
     /* Originate - this comes from the last packet the source sent us */
     message.originate_ts = interleaved ? *remote_ntp_rx : *remote_ntp_tx;
 
-    /* Prepare random bits which will be added to the receive timestamp */
-    UTI_GetNtp64Fuzz(&ts_fuzz, precision);
+    do {
+      /* Prepare random bits which will be added to the receive timestamp */
+      UTI_GetNtp64Fuzz(&ts_fuzz, precision);
 
-    /* Receive - this is when we received the last packet from the source.
-       This timestamp will have been adjusted so that it will now look to
-       the source like we have been running on our latest estimate of
-       frequency all along */
-    UTI_TimespecToNtp64(&local_receive, &message.receive_ts, &ts_fuzz);
+      /* Receive - this is when we received the last packet from the source.
+         This timestamp will have been adjusted so that it will now look to
+         the source like we have been running on our latest estimate of
+         frequency all along */
+      UTI_TimespecToNtp64(&local_receive, &message.receive_ts, &ts_fuzz);
+
+      /* Do not send a packet with a non-zero receive timestamp equal to the
+         originate timestamp or previous receive timestamp */
+    } while (!UTI_IsZeroNtp64(&message.receive_ts) &&
+             UTI_IsEqualAnyNtp64(&message.receive_ts, &message.originate_ts,
+                                 local_ntp_rx, NULL));
   } else {
     UTI_ZeroNtp64(&message.originate_ts);
     UTI_ZeroNtp64(&message.receive_ts);
@@ -1064,10 +1073,16 @@ transmit_packet(NTP_Mode my_mode, /* The mode this machine wants to be */
                           &message.transmit_ts, &ts_fuzz);
     }
 
-    /* Avoid sending messages with non-zero transmit timestamp equal to the
-       receive timestamp to allow reliable detection of the interleaved mode */
-  } while (!UTI_CompareNtp64(&message.transmit_ts, &message.receive_ts) &&
-           !UTI_IsZeroNtp64(&message.transmit_ts));
+    /* Do not send a packet with a non-zero transmit timestamp which is
+       equal to any of the following timestamps:
+       - receive (to allow reliable detection of the interleaved mode)
+       - originate (to prevent the packet from being its own valid response
+                    in the symmetric mode)
+       - previous transmit (to invalidate responses to the previous packet)
+       (the precision must be at least -30 to prevent an infinite loop!) */
+  } while (!UTI_IsZeroNtp64(&message.transmit_ts) &&
+           UTI_IsEqualAnyNtp64(&message.transmit_ts, &message.receive_ts,
+                               &message.originate_ts, local_ntp_tx));
 
   ret = NIO_SendPacket(&message, where_to, from, length, local_tx != NULL);
 
diff --git a/util.c b/util.c
index 586dcbd..95c27c0 100644
--- a/util.c
+++ b/util.c
@@ -726,6 +726,23 @@ UTI_CompareNtp64(NTP_int64 *a, NTP_int64 *b)
 
 /* ================================================== */
 
+int
+UTI_IsEqualAnyNtp64(NTP_int64 *a, NTP_int64 *b1, NTP_int64 *b2, NTP_int64 *b3)
+{
+  if (b1 && a->lo == b1->lo && a->hi == b1->hi)
+    return 1;
+
+  if (b2 && a->lo == b2->lo && a->hi == b2->hi)
+    return 1;
+
+  if (b3 && a->lo == b3->lo && a->hi == b3->hi)
+    return 1;
+
+  return 0;
+}
+
+/* ================================================== */
+
 /* Seconds part of NTP timestamp correponding to the origin of the time_t format */
 #define JAN_1970 0x83aa7e80UL
 
diff --git a/util.h b/util.h
index 02d598b..40ff729 100644
--- a/util.h
+++ b/util.h
@@ -136,6 +136,10 @@ extern int UTI_IsZeroNtp64(NTP_int64 *ts);
    b, and 1 if a is after b. */
 extern int UTI_CompareNtp64(NTP_int64 *a, NTP_int64 *b);
 
+/* Compare an NTP timestamp with up to three other timestamps.  Returns 0
+   if a is not equal to any of b1, b2, and b3, 1 otherwise. */
+extern int UTI_IsEqualAnyNtp64(NTP_int64 *a, NTP_int64 *b1, NTP_int64 *b2, NTP_int64 *b3);
+
 /* Convert a timespec into an NTP timestamp */
 extern void UTI_TimespecToNtp64(struct timespec *src, NTP_int64 *dest, NTP_int64 *fuzz);