diff --git a/src/scanpy/neighbors/__init__.py b/src/scanpy/neighbors/__init__.py
index 6338a7575e..9199394032 100644
--- a/src/scanpy/neighbors/__init__.py
+++ b/src/scanpy/neighbors/__init__.py
@@ -671,7 +671,7 @@ def _handle_transformer(
 
         # Validate `knn`
         conn_method = method if method in {"gauss", None} else "umap"
-        if not knn and not (conn_method == "gauss" and transformer is None):
+        if not knn and conn_method != "gauss":
             # “knn=False” seems to be only intended for method “gauss”
             msg = f"`method = {method!r} only with `knn = True`."
             raise ValueError(msg)
diff --git a/src/scanpy/neighbors/_backends/pairwise.py b/src/scanpy/neighbors/_backends/pairwise.py
index 19f6e472dc..485a895367 100644
--- a/src/scanpy/neighbors/_backends/pairwise.py
+++ b/src/scanpy/neighbors/_backends/pairwise.py
@@ -44,11 +44,16 @@ def transform(self, y: _MatrixLike | None) -> _CSMatrix:
         from sklearn.metrics import pairwise_distances
 
         d_arr = pairwise_distances(self.x_, y, metric=self.metric, **self.metric_params)
-        ind, dist = _get_indices_distances_from_dense_matrix(d_arr, self.n_neighbors)
+        ind, dist = _get_indices_distances_from_dense_matrix(
+            d_arr, self.n_neighbors + 1
+        )
         rv = _get_sparse_matrix_from_indices_distances(ind, dist, keep_self=True)
         if _DEBUG:
+            if self.n_neighbors >= d_arr.shape[1] - 1:
+                np.testing.assert_equal(d_arr, rv.toarray())
+
             ind2, dist2 = _get_indices_distances_from_sparse_matrix(
-                rv, self.n_neighbors
+                rv, self.n_neighbors + 1
             )
             np.testing.assert_equal(ind, ind2)
             np.testing.assert_equal(dist, dist2)
diff --git a/tests/test_neighbors.py b/tests/test_neighbors.py
index 0500eb6f9f..7ac6cb567d 100644
--- a/tests/test_neighbors.py
+++ b/tests/test_neighbors.py
@@ -147,6 +147,8 @@ def test_distances_euclidean(
     [
         # knn=False trivially returns all distances
         pytest.param(None, False, id="knn=False"),
+        # knn=False with pairwise returns all distances
+        pytest.param("sklearn-pairwise", False, id="pairwise"),
         # pynndescent returns all distances when data is so small
         pytest.param("pynndescent", True, id="pynndescent"),
         # Explicit brute force also returns all distances
@@ -157,7 +159,13 @@ def test_distances_euclidean(
         ),
     ],
 )
-def test_distances_all(neigh: Neighbors, transformer, knn):
+def test_distances_all(
+    monkeypatch: pytest.MonkeyPatch, neigh: Neighbors, transformer, knn
+):
+    from scanpy.neighbors._backends import pairwise
+
+    monkeypatch.setattr(pairwise, "_DEBUG", True)
+
     neigh.compute_neighbors(
         n_neighbors, transformer=transformer, method="gauss", knn=knn
     )