diff --git a/draco/analysis/flagging.py b/draco/analysis/flagging.py
index 2b57247a7..2c21b1ecb 100644
--- a/draco/analysis/flagging.py
+++ b/draco/analysis/flagging.py
@@ -1367,6 +1367,13 @@ class RFIMaskChisqHighDelay(task.SingleTask):
         from the median filtered version is greater than this number
         of expected standard deviations given the number of degrees
         of freedom (i.e., number of baselines).
+    estimate_var : bool
+        Estimate the variance in the test statistic using the median
+        absolute deviation over a region defined by the win_t and
+        win_f parameters.
+    only_positive : bool
+        Only mask large postive excursions in the test statistic,
+        leaving large negative excursions unmasked.
     """
 
     reg_arpls = config.Property(proptype=float, default=1e5)
@@ -1375,6 +1382,8 @@ class RFIMaskChisqHighDelay(task.SingleTask):
     win_t = config.Property(proptype=int, default=601)
     win_f = config.Property(proptype=int, default=1)
     nsigma_2d = config.Property(proptype=float, default=5.0)
+    estimate_var = config.Property(proptype=bool, default=False)
+    only_positive = config.Property(proptype=bool, default=False)
 
     def setup(self, telescope=None):
         """Save telescope object for time calculations.
@@ -1394,7 +1403,8 @@ def process(self, stream):
 
         Parameters
         ----------
-        stream : dcontainers.TimeStream | dcontainers.SiderealStream
+        stream : dcontainers.TimeStream | dcontainers.SiderealStream |
+                 dcontainers.HybridVisStream | dcontainers.RingMap
             Container holding a chi-squared test statistic in the visibility dataset.
             A weighted average will be taken over any axis that is not time/ra or frequency.
 
@@ -1430,19 +1440,29 @@ def process(self, stream):
         else:
             timestamp = stream.time
 
+        # Expand the weight dataset so that it can broadcast against the data dataset.
+        # Assumes that weight contains a subset of the axes in data, with the shared
+        # axes in the same order.  This is true for all of the supported input
+        # containers listed in the docstring.
+        dax = list(stream.data.attrs["axis"])
+        wax = list(stream.weight.attrs["axis"])
+        wshp = [stream.weight.shape[wax.index(ax)] if ax in wax else 1 for ax in dax]
+        wshp[dax.index("freq")] = None
+
+        # Extract the shape of the axes that are missing from the weights dataset,
+        # so that we can scale the denominator by this factor.
+        wshp_missing = [sz for sz, ax in zip(stream.data.shape, dax) if ax not in wax]
+        wfactor = np.prod(wshp_missing) if len(wshp_missing) > 0 else 1.0
+
         # Sum over any axis that is neither time nor frequency
         axsum = tuple(
-            [
-                ii
-                for ii, ax in enumerate(stream.vis.attrs["axis"])
-                if ax not in ["freq", "time", "ra"]
-            ]
+            [ii for ii, ax in enumerate(dax) if ax not in ["freq", "time", "ra"]]
         )
 
-        chisq = stream.vis[:].real
-        weight = stream.weight[:]
+        chisq = stream.data[:].real
+        weight = stream.weight[:].reshape(*wshp)
 
-        wsum = np.sum(weight, axis=axsum)
+        wsum = wfactor * np.sum(weight, axis=axsum)
         chisq = np.sum(weight * chisq, axis=axsum) * tools.invert_no_zero(wsum)
 
         # Gather all frequencies on all nodes
@@ -1553,7 +1573,21 @@ def mask_2d(self, y, w):
 
         # Calculate the deviation from the median, normalized by the
         # expected standard deviation
-        dy = np.abs(y - med_y) * np.sqrt(w)
+        dy = (y - med_y) * np.sqrt(w)
+
+        # If requested, estimate the variance in the test statistic
+        # using the median absolute deviation.
+        if self.estimate_var:
+            f = np.ascontiguousarray((w > 0.0).astype(np.float64))
+            mad_y = 1.48625 * weighted_median.moving_weighted_median(
+                np.abs(dy), f, win_size
+            )
+            dy *= tools.invert_no_zero(mad_y)
+
+        # Take the absolute value of the relative excursion unless
+        # explicitely requested to only flag positive excursions.
+        if not self.only_positive:
+            dy = np.abs(dy)
 
         # Flag times and frequencies that deviate by more than some threshold
         return dy > self.nsigma_2d