diff --git a/Tests/test_image_thumbnail.py b/Tests/test_image_thumbnail.py
index de15f5e2e98..f4ed8e746ff 100644
--- a/Tests/test_image_thumbnail.py
+++ b/Tests/test_image_thumbnail.py
@@ -38,9 +38,9 @@ def test_aspect():
     im.thumbnail((100, 50))
     assert im.size == (100, 50)
 
-    im = Image.new("L", (128, 128))
+    im = Image.new("L", (64, 64))
     im.thumbnail((100, 100))
-    assert im.size == (100, 100)
+    assert im.size == (64, 64)
 
     im = Image.new("L", (256, 162))  # ratio is 1.5802469136
     im.thumbnail((33, 33))
@@ -50,11 +50,23 @@ def test_aspect():
     im.thumbnail((33, 33))
     assert im.size == (21, 33)  # ratio is 0.6363636364
 
+    im = Image.new("L", (145, 100))  # ratio is 1.45
+    im.thumbnail((50, 50))
+    assert im.size == (50, 34)  # ratio is 1.47058823529
+
+    im = Image.new("L", (100, 145))  # ratio is 0.689655172414
+    im.thumbnail((50, 50))
+    assert im.size == (34, 50)  # ratio is 0.68
+
+    im = Image.new("L", (100, 30))  # ratio is 3.333333333333
+    im.thumbnail((75, 75))
+    assert im.size == (75, 23)  # ratio is 3.260869565217
+
 
 def test_float():
     im = Image.new("L", (128, 128))
     im.thumbnail((99.9, 99.9))
-    assert im.size == (100, 100)
+    assert im.size == (99, 99)
 
 
 def test_no_resize():
diff --git a/src/PIL/Image.py b/src/PIL/Image.py
index dec94f2d053..b1e8ad3ea06 100644
--- a/src/PIL/Image.py
+++ b/src/PIL/Image.py
@@ -2236,20 +2236,22 @@ def thumbnail(self, size, resample=BICUBIC, reducing_gap=2.0):
         :returns: None
         """
 
-        # preserve aspect ratio
-        x, y = self.size
-        if x > size[0]:
-            y = max(round(y * size[0] / x), 1)
-            x = round(size[0])
-        if y > size[1]:
-            x = max(round(x * size[1] / y), 1)
-            y = round(size[1])
-        size = x, y
-        box = None
-
-        if size == self.size:
+        x, y = map(math.floor, size)
+        if x >= self.width and y >= self.height:
             return
 
+        def round_aspect(number, key):
+            return max(min(math.floor(number), math.ceil(number), key=key), 1)
+
+        # preserve aspect ratio
+        aspect = self.width / self.height
+        if x / y >= aspect:
+            x = round_aspect(y * aspect, key=lambda n: abs(aspect - n / y))
+        else:
+            y = round_aspect(x / aspect, key=lambda n: abs(aspect - x / n))
+        size = (x, y)
+
+        box = None
         if reducing_gap is not None:
             res = self.draft(None, (size[0] * reducing_gap, size[1] * reducing_gap))
             if res is not None: