diff --git a/python_bindings/correctness/basics.py b/python_bindings/correctness/basics.py
index e4f3327d85c9..0bfa87ca6096 100644
--- a/python_bindings/correctness/basics.py
+++ b/python_bindings/correctness/basics.py
@@ -284,6 +284,22 @@ def test_vector_tile():
     p = hl.Pipeline([f, g])
     p.compile_jit()
 
+def test_scalar_funcs():
+    input = hl.ImageParam(hl.UInt(16), 0, 'input')
+
+    f = hl.Func('f')
+    g = hl.Func('g')
+
+    input[()]
+
+    (input[()]+input[()]) / 2
+    f[()]
+    g[()]
+
+    f[()] = (input[()]+input[()]+input[()])/3
+    g[()] = (f[()]+f[()]+f[()])/3
+
+    g.compile_jit()
 
 
 if __name__ == "__main__":
@@ -300,3 +316,4 @@ def test_vector_tile():
     test_basics3()
     test_basics4()
     test_basics5()
+    test_scalar_funcs()
diff --git a/python_bindings/correctness/buffer.py b/python_bindings/correctness/buffer.py
index cac68728a114..11ac31e49729 100644
--- a/python_bindings/correctness/buffer.py
+++ b/python_bindings/correctness/buffer.py
@@ -258,6 +258,19 @@ def test_buffer_to_str():
     b = hl.Buffer(hl.Int(32), [128, 256])
     assert str(b) == '<halide.Buffer of type int32 shape:[[0,128,1],[0,256,128]]>'
 
+def test_scalar_buffers():
+    buf = hl.Buffer.make_scalar(hl.Float(32))
+
+    assert buf.dimensions() == 0
+
+    buf.fill(0)
+    buf[()] = 2.5
+
+    assert buf[()] == 2.5
+
+    buf.fill(32)
+    assert buf[()] == 32
+
 if __name__ == "__main__":
     test_make_interleaved()
     test_interleaved_ndarray()
@@ -271,3 +284,4 @@ def test_buffer_to_str():
     test_reorder()
     test_overflow()
     test_buffer_to_str()
+    test_scalar_buffers()
diff --git a/python_bindings/readme.md b/python_bindings/readme.md
index 81224ed14bbd..e285a1716cab 100644
--- a/python_bindings/readme.md
+++ b/python_bindings/readme.md
@@ -8,7 +8,9 @@ with some differences where the C++ idiom is either inappropriate or impossible:
   offers variadic and list versions:
   `Buffer<>(Type t, int extent_dim_0, int extent_dim_1, ...., extent_dim_N, string name = "") Buffer<>(Type t, vector<int> extents, string name = "")`
   in Python, only the second variant is provided.
-- `Func` and `Buffer` access is done using `[]` rather than `()`
+- `Func` and `Buffer` access is done using `[]` rather than `()`.
+  - For zero-dimensional `Func` and `Buffer`, you must explicitly specify `[()]` -- that is, use an empty tuple as the index" --
+    as `[]` is not syntactically acceptable in Python.
 - Some classes in the Halide API aren't provided because they are 'wrapped' with
   standard Python idioms:
   - `Halide::Tuple` doesn't exist in the Python bindings; an ordinary Python