diff --git a/skimage/feature/peak.py b/skimage/feature/peak.py
index ebacfa3a..fe7ed081 100644
--- a/skimage/feature/peak.py
+++ b/skimage/feature/peak.py
@@ -10,6 +10,9 @@ def peak_local_max(image, min_distance=10, threshold='deprecated',
     Peaks are the local maxima in a region of `2 * min_distance + 1`
     (i.e. peaks are separated by at least `min_distance`).
 
+    NOTE: If peaks are flat (i.e. multiple pixels have exact same intensity),
+    the coordinates of all pixels are returned.
+
     Parameters
     ----------
     image: ndarray of floats
diff --git a/skimage/feature/tests/test_peak.py b/skimage/feature/tests/test_peak.py
index 7fb090ba..907370cc 100644
--- a/skimage/feature/tests/test_peak.py
+++ b/skimage/feature/tests/test_peak.py
@@ -43,6 +43,13 @@ def test_constant_image():
     assert len(peaks) == 0
 
 
+def test_flat_peak():
+    image = np.zeros((5, 5), dtype=np.uint8)
+    image[1:3, 1:3] = 10
+    peaks = peak.peak_local_max(image, min_distance=1)
+    assert len(peaks) == 4
+
+
 if __name__ == '__main__':
     from numpy import testing
     testing.run_module_suite()