diff --git a/CHANGES.rst b/CHANGES.rst
index 40c6d1230..def453bff 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -54,6 +54,9 @@ Changes
   :pr:`2096` by :user:`Ayesha Siddiqua <siddiqua-tamk>`.
 - The :class:`TableReport` can now be exported in markdown format with ``.markdown``.
   :pr:`2048` by :user:`Riccardo Cappuzzo <rcap107>`.
+- The :class:`DropUninformative` was improved so that `drop_if_constant` becomes a variance
+  threshold and it acts similarly to the VarianceThreshold transformer.
+  :pr:`2155` by :user:`Janne de Melo Santana <jannesantana>`, :user:`Xixi Khamsane<XIXI1234-creator>`, :user:`Rim El Khader<Rim-e>`
 
 Bugfixes
 --------
diff --git a/skrub/_drop_uninformative.py b/skrub/_drop_uninformative.py
index e20e07e93..21119831a 100644
--- a/skrub/_drop_uninformative.py
+++ b/skrub/_drop_uninformative.py
@@ -85,10 +85,12 @@ def __init__(
         drop_if_constant=False,
         drop_if_unique=False,
         drop_null_fraction=1.0,
+        threshold=0.0,
     ):
         self.drop_if_constant = drop_if_constant
         self.drop_if_unique = drop_if_unique
         self.drop_null_fraction = drop_null_fraction
+        self.threshold = threshold
 
     def _check_params(self):
         if not isinstance(self.drop_if_constant, bool):
@@ -127,8 +129,19 @@ def _drop_if_too_many_nulls(self, column):
 
     def _drop_if_constant(self, column):
         if self.drop_if_constant:
-            if (sbd.n_unique(column) == 1) and (self._null_count == 0):
+            if sbd.is_numeric(column) == 1 and (
+                self._null_count == 0
+            ):  # if numeric or boolean
+                if (
+                    sbd.std(column) ** 2 <= self.threshold
+                ):  # check if passes the threshold
+                    return True
+                else:
+                    return False
+            elif (sbd.n_unique(column) == 1) and (self._null_count == 0):
+                # use the original logic to deal with the other cases
                 return True
+
         return False
 
     def _drop_if_unique(self, column):
diff --git a/skrub/tests/test_drop_uninformative.py b/skrub/tests/test_drop_uninformative.py
index e3f04cacd..e2f0b062b 100644
--- a/skrub/tests/test_drop_uninformative.py
+++ b/skrub/tests/test_drop_uninformative.py
@@ -130,6 +130,7 @@ def drop_if_constant_table(df_module):
                 "const",
                 None,
             ],
+            "low_variance": [0.01, 0.02, 0.05],
         }
     )
 
@@ -141,6 +142,7 @@ def drop_if_constant_table(df_module):
         (dict(drop_if_constant=True), "constant_float", []),
         (dict(drop_if_constant=True), "constant_float_with_nulls", [2.5, 2.5, np.nan]),
         (dict(drop_if_constant=True), "constant_str", []),
+        (dict(drop_if_constant=True, threshold=0.5), "low_variance", []),
         (
             dict(drop_if_constant=True),
             "constant_str_with_nulls",