diff --git a/hwclock.c b/hwclock.c
index e2f72e7..06515e7 100644
--- a/hwclock.c
+++ b/hwclock.c
@@ -49,6 +49,7 @@
 #define DELAY_QUANT_MAX_K 2
 #define DELAY_QUANT_Q 10
 #define DELAY_QUANT_REPEAT 7
+#define DELAY_QUANT_LARGE_STEP_DELAY 1000
 #define DELAY_QUANT_MIN_STEP 1.0e-9
 
 struct HCL_Instance_Record {
@@ -127,6 +128,7 @@ HCL_CreateInstance(int min_samples, int max_samples, double min_separation, doub
   clock->precision = precision;
   clock->delay_quants = QNT_CreateInstance(DELAY_QUANT_MIN_K, DELAY_QUANT_MAX_K,
                                            DELAY_QUANT_Q, DELAY_QUANT_REPEAT,
+                                           DELAY_QUANT_LARGE_STEP_DELAY,
                                            DELAY_QUANT_MIN_STEP);
 
   LCL_AddParameterChangeHandler(handle_slew, clock);
diff --git a/ntp_core.c b/ntp_core.c
index e802e18..19b70a9 100644
--- a/ntp_core.c
+++ b/ntp_core.c
@@ -286,6 +286,7 @@ static ARR_Instance broadcasts;
 
 /* Parameters for the peer delay quantile */
 #define DELAY_QUANT_Q 100
+#define DELAY_QUANT_LARGE_STEP_DELAY 100
 #define DELAY_QUANT_REPEAT 7
 
 /* Minimum and maximum allowed poll interval */
@@ -690,6 +691,7 @@ NCR_CreateInstance(NTP_Remote_Address *remote_addr, NTP_Source_Type type,
   if (params->max_delay_quant > 0.0) {
     int k = round(CLAMP(0.05, params->max_delay_quant, 0.95) * DELAY_QUANT_Q);
     result->delay_quant = QNT_CreateInstance(k, k, DELAY_QUANT_Q, DELAY_QUANT_REPEAT,
+                                             DELAY_QUANT_LARGE_STEP_DELAY,
                                              LCL_GetSysPrecisionAsQuantum() / 2.0);
   } else {
     result->delay_quant = NULL;
diff --git a/quantiles.c b/quantiles.c
index f4783d4..3f0800d 100644
--- a/quantiles.c
+++ b/quantiles.c
@@ -49,19 +49,21 @@ struct QNT_Instance_Record {
   int q;
   int min_k;
   double min_step;
+  double neg_step_limit;
   int n_set;
 };
 
 /* ================================================== */
 
 QNT_Instance
-QNT_CreateInstance(int min_k, int max_k, int q, int repeat, double min_step)
+QNT_CreateInstance(int min_k, int max_k, int q, int repeat,
+                   int large_step_delay, double min_step)
 {
   QNT_Instance inst;
   long seed;
 
   if (q < 2 || min_k > max_k || min_k < 1 || max_k >= q ||
-      repeat < 1 || repeat > MAX_REPEAT || min_step <= 0.0)
+      repeat < 1 || repeat > MAX_REPEAT || min_step <= 0.0 || large_step_delay < 0)
     assert(0);
 
   inst = MallocNew(struct QNT_Instance_Record);
@@ -71,6 +73,7 @@ QNT_CreateInstance(int min_k, int max_k, int q, int repeat, double min_step)
   inst->q = q;
   inst->min_k = min_k;
   inst->min_step = min_step;
+  inst->neg_step_limit = -large_step_delay * min_step;
 
   QNT_Reset(inst);
 
@@ -136,7 +139,7 @@ insert_initial_value(QNT_Instance inst, double value)
 
 static void
 update_estimate(struct Quantile *quantile, double value, double p, double rand,
-                double min_step)
+                double min_step, double neg_step_limit)
 {
   if (value >= quantile->est) {
     if (rand < (1.0 - p))
@@ -163,6 +166,9 @@ update_estimate(struct Quantile *quantile, double value, double p, double rand,
       quantile->step = min_step;
     quantile->sign = -1;
   }
+
+  if (quantile->step < neg_step_limit)
+    quantile->step = neg_step_limit;
 }
 
 /* ================================================== */
@@ -183,7 +189,7 @@ QNT_Accumulate(QNT_Instance inst, double value)
     p = (double)(i / inst->repeat + inst->min_k) / inst->q;
     rand = (double)random() / ((1U << 31) - 1);
 
-    update_estimate(&inst->quants[i], value, p, rand, inst->min_step);
+    update_estimate(&inst->quants[i], value, p, rand, inst->min_step, inst->neg_step_limit);
   }
 }
 
diff --git a/quantiles.h b/quantiles.h
index b9665d5..bd335de 100644
--- a/quantiles.h
+++ b/quantiles.h
@@ -30,7 +30,8 @@
 
 typedef struct QNT_Instance_Record *QNT_Instance;
 
-extern QNT_Instance QNT_CreateInstance(int min_k, int max_k, int q, int repeat, double min_step);
+extern QNT_Instance QNT_CreateInstance(int min_k, int max_k, int q, int repeat,
+                                       int large_step_delay, double min_step);
 extern void QNT_DestroyInstance(QNT_Instance inst);
 
 extern void QNT_Reset(QNT_Instance inst);
diff --git a/test/unit/quantiles.c b/test/unit/quantiles.c
index e08801e..0462ec7 100644
--- a/test/unit/quantiles.c
+++ b/test/unit/quantiles.c
@@ -40,7 +40,7 @@ test_unit(void)
       max_k = random() % (q - 1) + 1;
     } while (min_k > max_k);
 
-    inst = QNT_CreateInstance(min_k, max_k, q, r, 1e-9);
+    inst = QNT_CreateInstance(min_k, max_k, q, r, 900, 1e-9);
 
     TEST_CHECK(min_k == QNT_GetMinK(inst));
     TEST_CHECK(max_k == QNT_GetMaxK(inst));
@@ -76,11 +76,11 @@ test_unit(void)
         TEST_CHECK(inst->quants[k].est > x - 0.4e-9);
         TEST_CHECK(inst->quants[k].est < x2 + 0.4e-9);
         TEST_CHECK(inst->quants[k].step < -15e-9);
-        TEST_CHECK(inst->quants[k].step > -1000e-9);
+        TEST_CHECK(inst->quants[k].step > -901e-9);
         if (min_k * 2 == q && k < inst->repeat) {
           if (x == x2) {
             TEST_CHECK(inst->quants[k].step < -750e-9);
-            TEST_CHECK(inst->quants[k].step > -1000e-9);
+            TEST_CHECK(inst->quants[k].step > -901e-9);
           } else {
             TEST_CHECK(inst->quants[k].step < -350e-9);
             TEST_CHECK(inst->quants[k].step > -600e-9);