diff --git a/Tests/test_image_getbbox.py b/Tests/test_image_getbbox.py
index af69ed57a..eec978210 100644
--- a/Tests/test_image_getbbox.py
+++ b/Tests/test_image_getbbox.py
@@ -1,3 +1,5 @@
+import pytest
+
 from PIL import Image
 
 from .helper import hopper
@@ -38,3 +40,16 @@ def test_bbox():
         for color in ((0, 0), (127, 0), (255, 0)):
             im = Image.new(mode, (100, 100), color)
             check(im, (255, 255))
+
+
+@pytest.mark.parametrize("mode", ("RGBA", "RGBa", "La", "LA", "PA"))
+def test_bbox_alpha_only_false(mode):
+    im = Image.new(mode, (100, 100))
+    assert im.getbbox(False) is None
+
+    fill_color = [1] * Image.getmodebands(mode)
+    fill_color[-1] = 0
+    im.paste(tuple(fill_color), (25, 25, 75, 75))
+    assert im.getbbox(False) == (25, 25, 75, 75)
+
+    assert im.getbbox() is None
diff --git a/src/PIL/Image.py b/src/PIL/Image.py
index bee9e23d0..f5d120671 100644
--- a/src/PIL/Image.py
+++ b/src/PIL/Image.py
@@ -1279,11 +1279,14 @@ class Image:
         """
         return ImageMode.getmode(self.mode).bands
 
-    def getbbox(self):
+    def getbbox(self, alpha_only=True):
         """
         Calculates the bounding box of the non-zero regions in the
         image.
 
+        :param alpha_only: Optional flag, defaulting to true.
+           If true and the image has an alpha channel, trim transparent pixels.
+           Otherwise, trim pixels when all channels are zero.
         :returns: The bounding box is returned as a 4-tuple defining the
            left, upper, right, and lower pixel coordinate. See
            :ref:`coordinate-system`. If the image is completely empty, this
@@ -1292,7 +1295,7 @@ class Image:
         """
 
         self.load()
-        return self.im.getbbox()
+        return self.im.getbbox(alpha_only)
 
     def getcolors(self, maxcolors=256):
         """