diff --git a/src/jacobi/_jacobi.py b/src/jacobi/_jacobi.py
index 4f06e07..2658bc0 100644
--- a/src/jacobi/_jacobi.py
+++ b/src/jacobi/_jacobi.py
@@ -64,7 +64,7 @@ def jacobi(
     """
     if diagonal:
         # TODO maybe solve this without introducing a wrapper function
-        return jacobi(
+        j, je = jacobi(
             lambda dx, x, *args: fn(x + dx, *args),
             0,
             x,
@@ -76,6 +76,10 @@ def jacobi(
             step=step,
             diagnostic=diagnostic,
         )
+        if mask is not None:
+            j[~mask] = 0.0
+            je[~mask] = 0.0
+        return j, je
 
     if maxiter <= 0:
         raise ValueError("maxiter must be > 0")
diff --git a/src/jacobi/_propagate.py b/src/jacobi/_propagate.py
index aac8851..e72cc71 100644
--- a/src/jacobi/_propagate.py
+++ b/src/jacobi/_propagate.py
@@ -178,16 +178,33 @@ def _propagate_independent(
 ):
     ycov: Union[float, np.ndarray] = 0
 
+    mask = kwargs.get("mask", None)
+    mask_parts = []
+    if mask is None:
+        kwargs2 = kwargs
+    else:
+        kwargs2 = kwargs.copy()
+        for i, x in enumerate(x_parts):
+            # this fails if mask is not indexable, but mask is always an array
+            if np.shape(x) == np.shape(mask[i]):
+                mask_parts.append(mask[i])
+            elif np.shape(x) == np.shape(mask):
+                mask_parts.append(mask)
+            else:
+                raise ValueError("mask shapes do not match arguments")
+
     for i, x in enumerate(x_parts):
-        rest = x_parts[:i] + x_parts[i + 1 :]
 
         def wrapped(x):
-            args = rest[:i] + [x] + rest[i:]
+            args = x_parts[:i] + [x] + x_parts[i + 1 :]
             return fn(*args)
 
         xcov = xcov_parts[i]
 
-        yc = _propagate(wrapped, y, x, xcov)[1]
+        if mask_parts:
+            kwargs2["mask"] = mask_parts[i]
+
+        yc = _propagate(wrapped, y, x, xcov, **kwargs2)[1]
         if np.ndim(ycov) == 2 and yc.ndim == 1:
             for i, yci in enumerate(yc):
                 ycov[i, i] += yci  # type:ignore
diff --git a/test/test_propagate.py b/test/test_propagate.py
index 4ca395f..09ee47f 100644
--- a/test/test_propagate.py
+++ b/test/test_propagate.py
@@ -2,6 +2,7 @@
 from numpy.testing import assert_allclose
 from jacobi import propagate, jacobi
 import pytest
+from numpy.testing import assert_equal
 
 
 def test_00():
@@ -218,7 +219,7 @@ def fn(x):
     assert_allclose(ycov, ycov_ref)
 
 
-def test_on_nan():
+def test_on_nan_1():
     def fn(x):
         return x**2 + 1
 
@@ -244,3 +245,66 @@ def fn(x):
     y2, ycov2 = propagate(fn, x, xcov)
     assert_allclose(y2, y_ref)
     assert_allclose(ycov2, ycov_ref)
+
+
+def test_on_nan_2():
+    nan = np.nan
+    a = np.array([4303.16536081, nan, 2586.42395464, nan, 2010.31141544, nan, nan, nan])
+    a_var = np.array(
+        [7.89977628e04, nan, 1.87676043e22, nan, 8.70294972e04, nan, nan, nan]
+    )
+    b = np.array([0.48358779, 0.0, 0.29371395, 0.0, 0.29838083, 0.58419942, 0.0, 0.0])
+    b_var = np.array(
+        [
+            2.31907643e-05,
+            0.00000000e00,
+            2.17812131e-05,
+            0.00000000e00,
+            2.82526004e-05,
+            1.66067899e-03,
+            0.00000000e00,
+            0.00000000e00,
+        ]
+    )
+
+    def f(a, b):
+        return a * b
+
+    c, c_var = propagate(f, a, a_var, b, b_var, diagonal=True)
+
+    mask = np.isnan(a) | np.isnan(b)
+    mask_var = mask | np.isnan(a_var) | np.isnan(b_var)
+    assert_equal(np.isnan(c), mask)
+    assert_equal(np.isnan(c_var), mask_var)
+
+
+def test_mask_on_binary_function_1():
+    a = np.array([1.0, 2.0])
+    a_var = 0.01 * a
+    b = np.array([3.0, 4.0])
+    b_var = 0.01 * b
+
+    def f(a, b):
+        return a * b
+
+    mask = [False, True]
+    c, c_var = propagate(f, a, a_var, b, b_var, mask=mask)
+
+    assert c_var[0] == 0
+    assert c_var[1] > 0
+
+
+def test_mask_on_binary_function_2():
+    a = np.array([1.0, 2.0])
+    a_var = 0.01 * a
+    b = np.array([3.0, 4.0, 5.0])
+    b_var = 0.01 * b
+
+    def f(a, b):
+        return np.outer(a, b).ravel()
+
+    mask = [[False, True], [True, False, True]]
+    c1, c1_var = propagate(f, a, a_var, b, b_var, mask=mask)
+    c2, c2_var = propagate(f, a, a_var, b, b_var)
+
+    assert np.sum(np.diag(c2_var) > np.diag(c1_var)) > 0