diff --git a/ntp.h b/ntp.h
index a61dd02..5a377ef 100644
--- a/ntp.h
+++ b/ntp.h
@@ -112,5 +112,6 @@ typedef struct {
 /* Special NTP reference IDs */
 #define NTP_REFID_UNSYNC 0x0UL
 #define NTP_REFID_LOCAL 0x7F7F0101UL /* 127.127.1.1 */
+#define NTP_REFID_SMOOTH 0x7F7F01FFUL /* 127.127.1.255 */
 
 #endif /* GOT_NTP_H */
diff --git a/ntp_core.c b/ntp_core.c
index 103d7c1..b477666 100644
--- a/ntp_core.c
+++ b/ntp_core.c
@@ -789,8 +789,8 @@ transmit_packet(NTP_Mode my_mode, /* The mode this machine wants to be */
 
   /* Get current smoothing offset when sending packet to a client */
   if (SMT_IsEnabled() && (my_mode == MODE_SERVER || my_mode == MODE_BROADCAST)) {
-    smooth_time = 1;
     smooth_offset = SMT_GetOffset(&local_transmit);
+    smooth_time = fabs(smooth_offset) > LCL_GetSysPrecisionAsQuantum();
 
     /* Suppress leap second when smoothing and slew mode are enabled */
     if (REF_GetLeapMode() == REF_LeapModeSlew &&
@@ -801,6 +801,14 @@ transmit_packet(NTP_Mode my_mode, /* The mode this machine wants to be */
     smooth_offset = 0.0;
   }
 
+  if (smooth_time) {
+    our_ref_id = NTP_REFID_SMOOTH;
+    UTI_AddDoubleToTimeval(&our_ref_time, smooth_offset, &our_ref_time);
+    UTI_AddDoubleToTimeval(local_rx, smooth_offset, &local_receive);
+  } else {
+    local_receive = *local_rx;
+  }
+
   if (are_we_synchronised) {
     leap = (int) leap_status;
   } else {
@@ -828,13 +836,6 @@ transmit_packet(NTP_Mode my_mode, /* The mode this machine wants to be */
 
   /* Now fill in timestamps */
 
-  if (smooth_time) {
-    UTI_AddDoubleToTimeval(&our_ref_time, smooth_offset, &our_ref_time);
-    UTI_AddDoubleToTimeval(local_rx, smooth_offset, &local_receive);
-  } else {
-    local_receive = *local_rx;
-  }
-
   UTI_TimevalToInt64(&our_ref_time, &message.reference_ts, 0);
 
   /* Originate - this comes from the last packet the source sent us */