diff --git a/test/test_utils.py b/test/test_utils.py
index ac394b51d63..e89bef4a6d9 100644
--- a/test/test_utils.py
+++ b/test/test_utils.py
@@ -355,6 +355,13 @@ def test_draw_keypoints_vanilla():
     assert_equal(img, img_cp)
 
 
+def test_draw_keypoins_K_equals_one():
+    # Non-regression test for https://github.com/pytorch/vision/pull/8439
+    img = torch.full((3, 100, 100), 0, dtype=torch.uint8)
+    keypoints = torch.tensor([[[10, 10]]], dtype=torch.float)
+    utils.draw_keypoints(img, keypoints)
+
+
 @pytest.mark.parametrize("colors", ["red", "#FF00FF", (1, 34, 122)])
 def test_draw_keypoints_colored(colors):
     # Keypoints is declared on top as global variable
diff --git a/torchvision/utils.py b/torchvision/utils.py
index 94b3ec65c87..6b2d19ec3dd 100644
--- a/torchvision/utils.py
+++ b/torchvision/utils.py
@@ -392,10 +392,10 @@ def draw_keypoints(
     # validate visibility
     if visibility is None:  # set default
         visibility = torch.ones(keypoints.shape[:-1], dtype=torch.bool)
-    # If the last dimension is 1, e.g., after calling split([2, 1], dim=-1) on the output of a keypoint-prediction
-    # model, make sure visibility has shape (num_instances, K).
-    # Iff K = 1, this has unwanted behavior, but K=1 does not really make sense in the first place.
-    visibility = visibility.squeeze(-1)
+    if visibility.ndim == 3:
+        # If visibility was passed as pred.split([2, 1], dim=-1), it will be of shape (num_instances, K, 1).
+        # We make sure it is of shape (num_instances, K). This isn't documented, we're just being nice.
+        visibility = visibility.squeeze(-1)
     if visibility.ndim != 2:
         raise ValueError(f"visibility must be of shape (num_instances, K). Got ndim={visibility.ndim}")
     if visibility.shape != keypoints.shape[:-1]: