diff --git a/Lib/test/list_tests.py b/Lib/test/list_tests.py
index ed63fda20c1b7a..36841eb3831563 100644
--- a/Lib/test/list_tests.py
+++ b/Lib/test/list_tests.py
@@ -281,6 +281,10 @@ def __length_hint__(self):
         a.extend(CustomIter())
         self.assertEqual(a, [1,2,3,4])
 
+        # bpo-28940
+        a = self.type2test([])
+        a.extend(CustomIter())
+        self.assertEqual(a, [])
 
     def test_insert(self):
         a = self.type2test([0, 1, 2])
diff --git a/Lib/test/test_bytes.py b/Lib/test/test_bytes.py
index 1408fb4fb84b0b..20d9a31561c5ea 100644
--- a/Lib/test/test_bytes.py
+++ b/Lib/test/test_bytes.py
@@ -774,6 +774,19 @@ def test_translate(self):
         c = b.translate(None, delete=b'e')
         self.assertEqual(c, b'hllo')
 
+    def test_from_iter(self):
+        # bpo-28940
+        class CustomIter:
+            def __iter__(self):
+                return self
+            def __next__(self):
+                raise StopIteration
+            def __length_hint__(self):
+                return sys.maxsize
+
+        a = self.type2test(CustomIter())
+        self.assertEqual(a, b'')
+
 
 class BytesTest(BaseBytesTest, unittest.TestCase):
     type2test = bytes
diff --git a/Lib/test/test_tuple.py b/Lib/test/test_tuple.py
index 84c064f19f2ec2..07567f3ee64806 100644
--- a/Lib/test/test_tuple.py
+++ b/Lib/test/test_tuple.py
@@ -3,6 +3,7 @@
 
 import gc
 import pickle
+import sys
 
 class TupleTest(seq_tests.CommonTest):
     type2test = tuple
@@ -223,5 +224,19 @@ def test_lexicographic_ordering(self):
         self.assertLess(a, b)
         self.assertLess(b, c)
 
+    def test_from_iter(self):
+        # bpo-28940
+        class CustomIter:
+            def __iter__(self):
+                return self
+            def __next__(self):
+                raise StopIteration
+            def __length_hint__(self):
+                return sys.maxsize
+
+        a = self.type2test(CustomIter())
+        self.assertEqual(a, ())
+
+
 if __name__ == "__main__":
     unittest.main()
diff --git a/Objects/abstract.c b/Objects/abstract.c
index 8d3030a118ae54..5e3117796b255d 100644
--- a/Objects/abstract.c
+++ b/Objects/abstract.c
@@ -1859,8 +1859,16 @@ PySequence_Tuple(PyObject *v)
     if (n == -1)
         goto Fail;
     result = PyTuple_New(n);
-    if (result == NULL)
-        goto Fail;
+    if (result == NULL) {
+        /* bpo-28940 - LengthHint could lie and asked for too much,
+         * try again without preallocation. */
+        PyErr_Clear();
+        result = PyTuple_New(0);
+        if (result == NULL) {
+            return NULL;
+        }
+        n = 0;
+    }
 
     /* Fill the tuple. */
     for (j = 0; ; ++j) {
diff --git a/Objects/bytearrayobject.c b/Objects/bytearrayobject.c
index 4e2bb603151b92..ff05ffb36d1eae 100644
--- a/Objects/bytearrayobject.c
+++ b/Objects/bytearrayobject.c
@@ -1639,8 +1639,15 @@ bytearray_extend(PyByteArrayObject *self, PyObject *iterable_of_ints)
 
     bytearray_obj = PyByteArray_FromStringAndSize(NULL, buf_size);
     if (bytearray_obj == NULL) {
-        Py_DECREF(it);
-        return NULL;
+        /* bpo-28940 - LengthHint could lie and asked for too much,
+         * try again without preallocation. */
+        PyErr_Clear();
+        bytearray_obj = PyByteArray_FromStringAndSize(NULL, 1);
+        if (bytearray_obj == NULL) {
+            Py_DECREF(it);
+            return NULL;
+        }
+        buf_size = 1;
     }
     buf = PyByteArray_AS_STRING(bytearray_obj);
 
diff --git a/Objects/bytesobject.c b/Objects/bytesobject.c
index 648b2a591516c1..32e7a3a4358b7d 100644
--- a/Objects/bytesobject.c
+++ b/Objects/bytesobject.c
@@ -2698,8 +2698,16 @@ _PyBytes_FromIterator(PyObject *it, PyObject *x)
 
     _PyBytesWriter_Init(&writer);
     str = _PyBytesWriter_Alloc(&writer, size);
-    if (str == NULL)
-        return NULL;
+    if (str == NULL) {
+        /* bpo-28940 - LengthHint could lie and asked for too much,
+         * try again without preallocation. */
+        PyErr_Clear();
+        _PyBytesWriter_Init(&writer);
+        str = _PyBytesWriter_Alloc(&writer, 1);
+        if (str == NULL) {
+            return NULL;
+        }
+    }
     writer.overallocate = 1;
     size = writer.allocated;
 
diff --git a/Objects/listobject.c b/Objects/listobject.c
index 4108f502023ad0..200657bd2006fe 100644
--- a/Objects/listobject.c
+++ b/Objects/listobject.c
@@ -886,10 +886,15 @@ list_extend(PyListObject *self, PyObject *iterable)
     else {
         mn = m + n;
         /* Make room. */
-        if (list_resize(self, mn) < 0)
-            goto error;
-        /* Make the list sane again. */
-        Py_SIZE(self) = m;
+        if (list_resize(self, mn) < 0) {
+            /* bpo-28940 - LengthHint could lie and asked for too much,
+             * try again without preallocation. */
+            PyErr_Clear();
+        }
+        else {
+            /* Make the list sane again. */
+            Py_SIZE(self) = m;
+        }
     }
 
     /* Run iterator to exhaustion. */