diff --git a/symmer/operators/anticommuting_op.py b/symmer/operators/anticommuting_op.py
index 7c550d0..fae497e 100644
--- a/symmer/operators/anticommuting_op.py
+++ b/symmer/operators/anticommuting_op.py
@@ -20,8 +20,9 @@ def __init__(self,
         super().__init__(AC_op_symp_matrix, coeff_list)
 
         # check all operators anticommute
-        anti_comm_check = self.adjacency_matrix.astype(int) - np.eye(self.adjacency_matrix.shape[0])
-        assert (np.sum(anti_comm_check) == 0), 'operator needs to be made of anti-commuting Pauli operators'
+        adj_mat = self.adjacency_matrix
+        adj_mat[np.diag_indices_from(adj_mat)] = False
+        assert ~np.any(adj_mat), 'operator needs to be made of anti-commuting Pauli operators'
 
         self.X_sk_rotations = []
         self.R_LCU = None
diff --git a/symmer/operators/base.py b/symmer/operators/base.py
index 82249f4..526a654 100644
--- a/symmer/operators/base.py
+++ b/symmer/operators/base.py
@@ -975,6 +975,14 @@ def commutes_termwise(self,
             np.array: A Boolean array indicating the term-wise commutation.
         """
         assert (self.n_qubits == PwordOp.n_qubits), 'Pauliwords defined for different number of qubits'
+
+        ### sparse code
+        # adjacency_matrix = (
+        #             csr_matrix(self.symp_matrix.astype(int)) @ csr_matrix(np.hstack((PwordOp.Z_block, PwordOp.X_block)).astype(int)).T)
+        # adjacency_matrix.data = ((adjacency_matrix.data % 2) != 0)
+        # return np.logical_not(adjacency_matrix.toarray())
+
+        ### dense code
         Omega_PwordOp_symp = np.hstack((PwordOp.Z_block,  PwordOp.X_block)).astype(int)
         return (self.symp_matrix @ Omega_PwordOp_symp.T) % 2 == 0
 
@@ -1089,6 +1097,14 @@ def is_noncontextual(self) -> bool:
             bool: True if the operator is noncontextual, False if contextual.
         """
         # if generators of operator (self) are noncontextual then whole of operator (self) must be too!
+        if self.n_terms<= 2*self.n_qubits+1:
+            # check edge case where all terms are anticommuting
+            adj_mat = self.adjacency_matrix
+            adj_mat[np.diag_indices_from(adj_mat)] = False
+            if ~np.any(adj_mat):
+                # operator is all anticommuting
+                return True
+
         from symmer.utils import get_generators_including_xz_products
         xyz_generators = get_generators_including_xz_products(self)
 
diff --git a/tests/test_operators/test_base.py b/tests/test_operators/test_base.py
index f271698..8c87cb4 100644
--- a/tests/test_operators/test_base.py
+++ b/tests/test_operators/test_base.py
@@ -650,6 +650,25 @@ def test_is_noncontextual_generators():
     # assert check_adjmat_noncontextual(Hnc.generators.adjacency_matrix), 'noncontexutal operator is being correctly defined as noncontextual'
     assert Hnc.is_noncontextual, 'noncontexutal operator is being correctly defined as noncontextual'
 
+def test_is_noncontextual_anticommuting_H():
+    """
+    noncontextual test that breaks if only 2n generators are used rather than 3n generators
+    Returns:
+
+    """
+    Hnc = PauliwordOp.from_dictionary({
+             'ZZZI': (1.2532436410975218-0j),
+             'IIXI': (0.8935108507410493-0j),
+             'ZIYI': (-1.1362909076230914+0j),
+             'IXZI': (-0.05373661687140326+0j),
+             'ZYZI': (-1.0012312990477774+0j),
+             'XXYI': (-0.045809456087963205+0j),
+             'YXYZ': (0.21569499626612557-0j),
+             'YXYX': (-0.5806963175396661+0j),
+             'YXYY': (0.3218493853030614-0j)})
+
+    assert Hnc.is_noncontextual, 'noncontexutal operator is being correctly defined as noncontextual'
+
 def test_multiplication_1():
     """ Tests multiplication and the OpenFermion conversion
     """