diff --git a/healpix_convolution/kernels/common.py b/healpix_convolution/kernels/common.py
index 9f4d548..04bc30d 100644
--- a/healpix_convolution/kernels/common.py
+++ b/healpix_convolution/kernels/common.py
@@ -4,8 +4,9 @@
 import sparse
 
 
-def create_sparse(cell_ids, neighbours, weights):
+def create_sparse(cell_ids, neighbours, weights, weights_threshold=None):
     neighbours_ = np.reshape(neighbours, (-1,))
+    reshaped_weights = np.reshape(weights, (-1,))
 
     all_cell_ids = np.unique(neighbours_)
     if all_cell_ids[0] == -1:
@@ -20,8 +21,10 @@ def create_sparse(cell_ids, neighbours, weights):
     coords = np.stack([row_indices, column_indices], axis=0)
 
     mask = neighbours_ != -1
+    if weights_threshold is not None:
+        mask = np.logical_and(mask, np.abs(reshaped_weights) >= weights_threshold)
 
-    weights_ = np.reshape(weights, (-1,))[mask]
+    weights_ = reshaped_weights[mask]
     coords_ = coords[..., mask]
 
     if isinstance(weights_, da.Array):
diff --git a/healpix_convolution/kernels/gaussian.py b/healpix_convolution/kernels/gaussian.py
index 03867e3..f77c662 100644
--- a/healpix_convolution/kernels/gaussian.py
+++ b/healpix_convolution/kernels/gaussian.py
@@ -36,6 +36,7 @@ def gaussian_kernel(
     sigma: float,
     truncate: float = 4.0,
     kernel_size: int | None = None,
+    weights_threshold: float | None = None,
 ):
     """construct a gaussian kernel on the healpix grid
 
@@ -48,11 +49,13 @@ def gaussian_kernel(
     indexing_scheme : {"nested", "ring"}
         The healpix indexing scheme
     sigma : float
-        The standard deviation of the gaussian kernel
+        The standard deviation of the gaussian function in radians.
     truncate : float, default: 4.0
         Truncate the kernel after this many multiples of ``sigma``.
     kernel_size : int, optional
-        If given, determines the size of the kernel. In that case, ``truncate`` is ignored.
+        If given, will be used instead of ``truncate`` to determine the size of the kernel.
+    weights_threshold : float, optional
+        If given, drop all kernel weights whose absolute value is smaller than this threshold.
 
     Returns
     -------
@@ -78,4 +81,4 @@ def gaussian_kernel(
     d = angular_distances(nb, resolution=resolution, indexing_scheme=indexing_scheme)
     weights = gaussian_function(d, sigma, mask=nb == -1)
 
-    return create_sparse(cell_ids, nb, weights)
+    return create_sparse(cell_ids, nb, weights, weights_threshold)
diff --git a/healpix_convolution/tests/test_kernels.py b/healpix_convolution/tests/test_kernels.py
index b70184c..fa4de35 100644
--- a/healpix_convolution/tests/test_kernels.py
+++ b/healpix_convolution/tests/test_kernels.py
@@ -48,6 +48,55 @@ def test_create_sparse(cell_ids, neighbours, weights):
     assert actual.shape == expected_shape
 
 
+@pytest.mark.parametrize(
+    ["cell_ids", "neighbours", "threshold"],
+    (
+        pytest.param(
+            np.array([0, 1]),
+            np.array(
+                [[0, 17, 19, 2, 3, 1, 23, 22, 35], [3, 2, 13, 15, 11, 7, 6, 1, 0]]
+            ),
+            None,
+        ),
+        pytest.param(
+            np.array([0, 1]),
+            np.array(
+                [[0, 17, 19, 2, 3, 1, 23, 22, 35], [3, 2, 13, 15, 11, 7, 6, 1, 0]]
+            ),
+            0.1,
+        ),
+        pytest.param(
+            np.array([3, 2]),
+            np.array(
+                [[3, 2, 13, 15, 11, 7, 6, 1, 0], [2, 19, -1, 13, 15, 3, 1, 0, 17]]
+            ),
+            0.1,
+        ),
+    ),
+)
+def test_create_sparse_threshold(cell_ids, neighbours, threshold):
+    expected_cell_ids = np.unique(neighbours)
+    if expected_cell_ids[0] == -1:
+        expected_cell_ids = expected_cell_ids[1:]
+
+    weights = np.reshape(neighbours / np.sum(neighbours, axis=1, keepdims=True), (-1,))
+
+    actual_cell_ids, actual = np_kernels.common.create_sparse(
+        cell_ids, neighbours, weights, weights_threshold=threshold
+    )
+
+    expected_nnz = (
+        np.sum(abs(weights) >= threshold) if threshold is not None else weights.size
+    )
+
+    np.testing.assert_equal(actual_cell_ids, expected_cell_ids)
+
+    expected_shape = (cell_ids.size, expected_cell_ids.size)
+    assert hasattr(actual, "nnz"), "not a sparse matrix"
+    assert actual.shape == expected_shape
+    assert actual.nnz == expected_nnz, "non-zero entries don't match"
+
+
 def fit_polynomial(x, y, deg):
     mask = y > 0
     x_ = x[mask]
diff --git a/healpix_convolution/xarray/kernels/gaussian.py b/healpix_convolution/xarray/kernels/gaussian.py
index f58ddb8..e50f252 100644
--- a/healpix_convolution/xarray/kernels/gaussian.py
+++ b/healpix_convolution/xarray/kernels/gaussian.py
@@ -15,7 +15,11 @@ def compute_ring(grid_info, sigma, kernel_size, truncate):
 
 
 def gaussian_kernel(
-    cell_ids, sigma: float, truncate: float = 4.0, kernel_size: int | None = None
+    cell_ids,
+    sigma: float,
+    truncate: float = 4.0,
+    kernel_size: int | None = None,
+    weights_threshold: float | None = None,
 ):
     """Create a symmetric gaussian kernel for the given cell ids
 
@@ -26,9 +30,12 @@ def gaussian_kernel(
     sigma : float
         The standard deviation of the gaussian function in radians.
     truncate : float, default: 4.0
-        Truncate the kernel after this many multiples of sigma.
+        Truncate the kernel after this many multiples of ``sigma``.
     kernel_size : int, optional
         If given, will be used instead of ``truncate`` to determine the size of the kernel.
+    weights_threshold : float, optional
+        If given, drop all kernel weights whose absolute value is smaller than this threshold.
+
 
     Returns
     -------
@@ -44,6 +51,7 @@ def gaussian_kernel(
         sigma=sigma,
         truncate=truncate,
         kernel_size=kernel_size,
+        weights_threshold=weights_threshold,
     )
 
     if kernel_size is not None: