diff --git a/moto/s3/responses.py b/moto/s3/responses.py
index 3fe391cd3..adaefc230 100644
--- a/moto/s3/responses.py
+++ b/moto/s3/responses.py
@@ -252,13 +252,13 @@ class ResponseObject(_TemplateEnvironmentMixin):
         toint = lambda i: int(i) if i else None
         begin, end = map(toint, rspec.split('-'))
         if begin is not None:  # byte range
-            end = last if end is None else end
+            end = last if end is None else min(end, last)
         elif end is not None:  # suffix byte range
-            begin = length - end
+            begin = length - min(end, length)
             end = last
         else:
             return 400, headers, ""
-        if begin < 0 or end > length or begin > min(end, last):
+        if begin < 0 or end > last or begin > min(end, last):
             return 416, headers, ""
         headers['content-range'] = "bytes {0}-{1}/{2}".format(
             begin, end, length)
diff --git a/tests/test_s3/test_s3.py b/tests/test_s3/test_s3.py
index 662b22cbb..43f25c748 100644
--- a/tests/test_s3/test_s3.py
+++ b/tests/test_s3/test_s3.py
@@ -791,11 +791,35 @@ def test_ranged_get():
     key.key = 'bigkey'
     rep = b"0123456789"
     key.set_contents_from_string(rep * 10)
+
+    # Implicitly bounded range requests.
     key.get_contents_as_string(headers={'Range': 'bytes=0-'}).should.equal(rep * 10)
-    key.get_contents_as_string(headers={'Range': 'bytes=0-99'}).should.equal(rep * 10)
-    key.get_contents_as_string(headers={'Range': 'bytes=0-0'}).should.equal(b'0')
-    key.get_contents_as_string(headers={'Range': 'bytes=99-99'}).should.equal(b'9')
-    key.get_contents_as_string(headers={'Range': 'bytes=50-54'}).should.equal(rep[:5])
     key.get_contents_as_string(headers={'Range': 'bytes=50-'}).should.equal(rep * 5)
+    key.get_contents_as_string(headers={'Range': 'bytes=99-'}).should.equal(b'9')
+
+    # Explicitly bounded range requests starting from the first byte.
+    key.get_contents_as_string(headers={'Range': 'bytes=0-0'}).should.equal(b'0')
+    key.get_contents_as_string(headers={'Range': 'bytes=0-49'}).should.equal(rep * 5)
+    key.get_contents_as_string(headers={'Range': 'bytes=0-99'}).should.equal(rep * 10)
+    key.get_contents_as_string(headers={'Range': 'bytes=0-100'}).should.equal(rep * 10)
+    key.get_contents_as_string(headers={'Range': 'bytes=0-700'}).should.equal(rep * 10)
+
+    # Explicitly bounded range requests starting from the / a middle byte.
+    key.get_contents_as_string(headers={'Range': 'bytes=50-54'}).should.equal(rep[:5])
+    key.get_contents_as_string(headers={'Range': 'bytes=50-99'}).should.equal(rep * 5)
+    key.get_contents_as_string(headers={'Range': 'bytes=50-100'}).should.equal(rep * 5)
+    key.get_contents_as_string(headers={'Range': 'bytes=50-700'}).should.equal(rep * 5)
+
+    # Explicitly bounded range requests starting from the last byte.
+    key.get_contents_as_string(headers={'Range': 'bytes=99-99'}).should.equal(b'9')
+    key.get_contents_as_string(headers={'Range': 'bytes=99-100'}).should.equal(b'9')
+    key.get_contents_as_string(headers={'Range': 'bytes=99-700'}).should.equal(b'9')
+
+    # Suffix range requests.
+    key.get_contents_as_string(headers={'Range': 'bytes=-1'}).should.equal(b'9')
     key.get_contents_as_string(headers={'Range': 'bytes=-60'}).should.equal(rep * 6)
+    key.get_contents_as_string(headers={'Range': 'bytes=-100'}).should.equal(rep * 10)
+    key.get_contents_as_string(headers={'Range': 'bytes=-101'}).should.equal(rep * 10)
+    key.get_contents_as_string(headers={'Range': 'bytes=-700'}).should.equal(rep * 10)
+
     key.size.should.equal(100)