diff --git a/phc2sys.8 b/phc2sys.8
index 8e03e81..d7a4569 100644
--- a/phc2sys.8
+++ b/phc2sys.8
@@ -19,6 +19,10 @@ phc2sys \- synchronize two clocks
 ] [
 .BI \-I " ki"
 ] [
+.BI \-S " step"
+] [
+.BI \-F " step"
+] [
 .BI \-R " update-rate"
 ] [
 .BI \-N " clock-readings"
@@ -87,8 +91,16 @@ Specify the integral constant of the PI controller. The default is 0.3.
 .BI \-S " step"
 Specify the step threshold of the PI controller. It is the maximum offset that
 the controller corrects by changing the clock frequency instead of stepping the
-clock. The clock is always stepped on start. The value of 0.0 disables stepping
-after the start. The default is 0.0.
+clock. The clock is stepped on start regardless of the option if the offset is
+larger than 100 nanoseconds (unless the
+.BI \-F
+option is used). The value of 0.0 disables stepping after the start. The default
+is 0.0.
+.TP
+.BI \-F " step"
+Specify the step threshold applied only on the first update. It is the maximum
+offset that is corrected by adjusting clock. The value of 0.0 disables stepping
+on start. The default is 0.0000001 (100 nanoseconds).
 .TP
 .BI \-R " update-rate"
 Specify the slave clock update rate when running in the direct synchronization
diff --git a/phc2sys.c b/phc2sys.c
index 594fc1e..8f9e18b 100644
--- a/phc2sys.c
+++ b/phc2sys.c
@@ -555,6 +555,7 @@ static void usage(char *progname)
 		" -P [kp]        proportional constant (0.7)\n"
 		" -I [ki]        integration constant (0.3)\n"
 		" -S [step]      step threshold (disabled)\n"
+		" -F [step]      step threshold only on start (0.0000001)\n"
 		" -R [rate]      slave clock update rate in HZ (1.0)\n"
 		" -N [num]       number of master clock readings per update (5)\n"
 		" -O [offset]    slave-master time offset (0)\n"
@@ -593,7 +594,7 @@ int main(int argc, char *argv[])
 	progname = strrchr(argv[0], '/');
 	progname = progname ? 1+progname : argv[0];
 	while (EOF != (c = getopt(argc, argv,
-				  "c:d:hs:P:I:S:R:N:O:i:u:wn:xl:mqv"))) {
+				  "c:d:s:P:I:S:F:R:N:O:i:u:wn:xl:mqvh"))) {
 		switch (c) {
 		case 'c':
 			dst_clock.clkid = clock_open(optarg);
@@ -627,6 +628,11 @@ int main(int argc, char *argv[])
 					  0.0, DBL_MAX))
 				return -1;
 			break;
+		case 'F':
+			if (get_arg_val_d(c, optarg, &configured_pi_f_offset,
+					  0.0, DBL_MAX))
+				return -1;
+			break;
 		case 'R':
 			if (get_arg_val_d(c, optarg, &phc_rate, 0.0, DBL_MAX))
 				return -1;
diff --git a/pi.c b/pi.c
index 78cbd3f..89080c4 100644
--- a/pi.c
+++ b/pi.c
@@ -35,6 +35,7 @@
 double configured_pi_kp = 0.0;
 double configured_pi_ki = 0.0;
 double configured_pi_offset = 0.0;
+double configured_pi_f_offset = 0.0000001; /* 100 nanoseconds */
 int configured_pi_max_freq = 900000000;
 
 struct pi_servo {
@@ -46,7 +47,9 @@ struct pi_servo {
 	double kp;
 	double ki;
 	double max_offset;
+	double max_f_offset;
 	int count;
+	int first_update;
 };
 
 static void pi_destroy(struct servo *servo)
@@ -88,7 +91,14 @@ static double pi_sample(struct servo *servo,
 		else if (s->drift > s->maxppb)
 			s->drift = s->maxppb;
 
-		*state = SERVO_JUMP;
+		if (!s->first_update ||
+		    (s->max_f_offset && (s->max_f_offset < fabs(offset))) ||
+		    (s->max_offset && (s->max_offset < fabs(offset))))
+			*state = SERVO_JUMP;
+		else
+			*state = SERVO_LOCKED;
+
+		s->first_update = 0;
 		ppb = s->drift;
 		s->count = 2;
 		break;
@@ -134,6 +144,7 @@ struct servo *pi_servo_create(int fadj, int max_ppb, int sw_ts)
 	s->servo.sample  = pi_sample;
 	s->drift         = fadj;
 	s->maxppb        = max_ppb;
+	s->first_update  = 1;
 
 	if (configured_pi_kp && configured_pi_ki) {
 		s->kp = configured_pi_kp;
@@ -152,6 +163,12 @@ struct servo *pi_servo_create(int fadj, int max_ppb, int sw_ts)
 		s->max_offset = 0.0;
 	}
 
+	if (configured_pi_f_offset > 0.0) {
+		s->max_f_offset = configured_pi_f_offset * NSEC_PER_SEC;
+	} else {
+		s->max_f_offset = 0.0;
+	}
+
 	if (configured_pi_max_freq && s->maxppb > configured_pi_max_freq) {
 		s->maxppb = configured_pi_max_freq;
 	}
diff --git a/pi.h b/pi.h
index 954f495..2f31bce 100644
--- a/pi.h
+++ b/pi.h
@@ -36,12 +36,21 @@ extern double configured_pi_ki;
 /**
  * When set to a non-zero value, this variable controls the maximum allowed
  * offset before a clock jump occurs instead of the default clock-slewing
- * mechanism
+ * mechanism.
  *
  * Note that this variable is measured in seconds, and allows fractional values.
  */
 extern double configured_pi_offset;
 
+/**
+ * When set to zero, the clock is not stepped on start. When set to a non-zero
+ * value, the value bahaves as a threshold and the clock is stepped on start if
+ * the offset is bigger than the threshold.
+ *
+ * Note that this variable is measured in seconds, and allows fractional values.
+ */
+extern double configured_pi_f_offset;
+
 /**
  * When set to a non-zero value, this variable sets an additional limit for
  * the frequency adjustment of the clock. It's in ppb.