diff --git a/refclock.c b/refclock.c
index 0ccb30a..888c488 100644
--- a/refclock.c
+++ b/refclock.c
@@ -53,6 +53,8 @@ struct MedianFilter {
   int index;
   int used;
   int last;
+  int avg_var_n;
+  double avg_var;
   struct FilterSample *samples;
   int *selected;
   double *x_data;
@@ -101,6 +103,7 @@ static void log_sample(RCL_Instance instance, struct timeval *sample_time, int f
 static void filter_init(struct MedianFilter *filter, int length);
 static void filter_fini(struct MedianFilter *filter);
 static void filter_reset(struct MedianFilter *filter);
+static double filter_get_avg_sample_dispersion(struct MedianFilter *filter);
 static void filter_add_sample(struct MedianFilter *filter, struct timeval *sample_time, double offset, double dispersion);
 static int filter_get_last_sample(struct MedianFilter *filter, struct timeval *sample_time, double *offset, double *dispersion);
 static int filter_select_samples(struct MedianFilter *filter);
@@ -348,7 +351,7 @@ RCL_AddSample(RCL_Instance instance, struct timeval *sample_time, double offset,
 
   LCL_GetOffsetCorrection(sample_time, &correction, &dispersion);
   UTI_AddDoubleToTimeval(sample_time, correction, &cooked_time);
-  dispersion += LCL_GetSysPrecisionAsQuantum();
+  dispersion += LCL_GetSysPrecisionAsQuantum() + filter_get_avg_sample_dispersion(&instance->filter);
 
   if (!valid_sample_time(instance, sample_time))
     return 0;
@@ -374,7 +377,7 @@ RCL_AddPulse(RCL_Instance instance, struct timeval *pulse_time, double second)
 
   LCL_GetOffsetCorrection(pulse_time, &correction, &dispersion);
   UTI_AddDoubleToTimeval(pulse_time, correction, &cooked_time);
-  dispersion += LCL_GetSysPrecisionAsQuantum();
+  dispersion += LCL_GetSysPrecisionAsQuantum() + filter_get_avg_sample_dispersion(&instance->filter);
 
   if (!valid_sample_time(instance, pulse_time))
     return 0;
@@ -526,7 +529,6 @@ poll_timeout(void *arg)
     int sample_ok, stratum;
 
     sample_ok = filter_get_sample(&inst->filter, &sample_time, &offset, &dispersion);
-    filter_reset(&inst->filter);
     inst->driver_polled = 0;
 
     if (sample_ok) {
@@ -634,6 +636,9 @@ filter_init(struct MedianFilter *filter, int length)
   filter->index = -1;
   filter->used = 0;
   filter->last = -1;
+  /* set first estimate to system precision */
+  filter->avg_var_n = 0;
+  filter->avg_var = LCL_GetSysPrecisionAsQuantum() * LCL_GetSysPrecisionAsQuantum();
   filter->samples = MallocArray(struct FilterSample, filter->length);
   filter->selected = MallocArray(int, filter->length);
   filter->x_data = MallocArray(double, filter->length);
@@ -658,6 +663,12 @@ filter_reset(struct MedianFilter *filter)
   filter->used = 0;
 }
 
+static double
+filter_get_avg_sample_dispersion(struct MedianFilter *filter)
+{
+  return sqrt(filter->avg_var);
+}
+
 static void
 filter_add_sample(struct MedianFilter *filter, struct timeval *sample_time, double offset, double dispersion)
 {
@@ -789,8 +800,8 @@ static int
 filter_get_sample(struct MedianFilter *filter, struct timeval *sample_time, double *offset, double *dispersion)
 {
   struct FilterSample *s, *ls;
-  int i, n;
-  double x, y, d, e;
+  int i, n, dof;
+  double x, y, d, e, var, prev_avg_var;
 
   n = filter_select_samples(filter);
 
@@ -818,6 +829,8 @@ filter_get_sample(struct MedianFilter *filter, struct timeval *sample_time, doub
   y /= n;
   e /= n;
 
+  e -= sqrt(filter->avg_var);
+
   if (n >= 4) {
     double b0, b1, s2, sb0, sb1;
 
@@ -829,18 +842,53 @@ filter_get_sample(struct MedianFilter *filter, struct timeval *sample_time, doub
        as dispersion */
     RGR_WeightedRegression(filter->x_data, filter->y_data, filter->w_data, n,
         &b0, &b1, &s2, &sb0, &sb1);
+    var = s2;
     d = sb0;
+    dof = n - 2;
   } else if (n >= 2) {
     for (i = 0, d = 0.0; i < n; i++)
       d += (filter->y_data[i] - y) * (filter->y_data[i] - y);
-    d = sqrt(d / (n - 1));
+    var = d / (n - 1);
+    d = sqrt(var);
+    dof = n - 1;
   } else {
-    d = 0.0;
+    var = filter->avg_var;
+    d = sqrt(var);
+    dof = 1;
   }
 
+  /* avoid having zero dispersion */
+  if (var < 1e-20) {
+    var = 1e-20;
+    d = sqrt(var);
+  }
+
+  prev_avg_var = filter->avg_var;
+
+  /* update exponential moving average of the variance */
+  if (filter->avg_var_n > 100) {
+    filter->avg_var += dof / (dof + 100.0) * (var - filter->avg_var);
+  } else {
+    filter->avg_var = (filter->avg_var * filter->avg_var_n + var * dof) /
+      (dof + filter->avg_var_n);
+    if (filter->avg_var_n == 0)
+      prev_avg_var = filter->avg_var;
+    filter->avg_var_n += dof;
+  }
+
+  /* reduce noise in sourcestats weights by using the long-term average
+     instead of the estimated variance if it's not significantly lower */
+  if (var * dof / RGR_GetChi2Coef(dof) < prev_avg_var)
+    d = sqrt(filter->avg_var) * d / sqrt(var);
+
+  if (d < e)
+    d = e;
+
   UTI_AddDoubleToTimeval(&ls->sample_time, x, sample_time);
   *offset = y;
-  *dispersion = d + e;
+  *dispersion = d;
+
+  filter_reset(filter);
 
   return 1;
 }
diff --git a/regress.c b/regress.c
index 9a49db4..c870a19 100644
--- a/regress.c
+++ b/regress.c
@@ -135,6 +135,30 @@ RGR_GetTCoef(int dof)
   }
 }
 
+/* ================================================== */
+/* Get 90% quantile of chi-square distribution */
+
+double
+RGR_GetChi2Coef(int dof)
+{
+  static double coefs[] = {
+    2.706, 4.605, 6.251, 7.779, 9.236, 10.645, 12.017, 13.362,
+    14.684, 15.987, 17.275, 18.549, 19.812, 21.064, 22.307, 23.542,
+    24.769, 25.989, 27.204, 28.412, 29.615, 30.813, 32.007, 33.196,
+    34.382, 35.563, 36.741, 37.916, 39.087, 40.256, 41.422, 42.585,
+    43.745, 44.903, 46.059, 47.212, 48.363, 49.513, 50.660, 51.805,
+    52.949, 54.090, 55.230, 56.369, 57.505, 58.641, 59.774, 60.907,
+    62.038, 63.167, 64.295, 65.422, 66.548, 67.673, 68.796, 69.919,
+    71.040, 72.160, 73.279, 74.397, 75.514, 76.630, 77.745, 78.860
+  };
+
+  if (dof <= 64) {
+    return coefs[dof-1];
+  } else {
+    return 1.2 * dof; /* Until I can be bothered to do something better */
+  }
+}
+
 /* ================================================== */
 /* Structure used for holding results of each regression */
 
diff --git a/regress.h b/regress.h
index 9e3d3ca..cd75c5c 100644
--- a/regress.h
+++ b/regress.h
@@ -61,6 +61,11 @@ RGR_WeightedRegression
 
 extern double RGR_GetTCoef(int dof);
 
+/* Return the value to apply to the variance to make an upper one-sided
+   test assuming a chi-square distribution. */
+
+extern double RGR_GetChi2Coef(int dof);
+
 /* Return a status indicating whether there were enough points to
    carry out the regression */