diff -r 785e29d8ce13 Lib/test/test_set.py
--- a/Lib/test/test_set.py	Wed May 14 23:37:14 2014 +0200
+++ b/Lib/test/test_set.py	Thu May 15 00:14:15 2014 +0200
@@ -361,6 +361,20 @@ class TestJointOps:
         gc.collect()
         self.assertTrue(ref() is None, "Cycle was not collected")
 
+    @support.cpython_only
+    def test_length_hint(self):
+        # Issue #21507: set constructor should use operator.length_hint to
+        # guess the final length, and so limit the overallocation of the set
+        for n in (10, 100, 500, 1000):
+            data = list(range(n))
+            fs1 = self.thetype(self.thetype(data))
+            fs2 = self.thetype(data)
+            self.assertEqual(sys.getsizeof(fs2), sys.getsizeof(fs1))
+            fs3 = self.thetype(iter(data))
+            self.assertEqual(sys.getsizeof(fs3), sys.getsizeof(fs1))
+            fs4 = self.thetype(iter(set(data)))
+            self.assertEqual(sys.getsizeof(fs4), sys.getsizeof(fs1))
+
 class TestSet(TestJointOps, unittest.TestCase):
     thetype = set
     basetype = set
diff -r 785e29d8ce13 Objects/setobject.c
--- a/Objects/setobject.c	Wed May 14 23:37:14 2014 +0200
+++ b/Objects/setobject.c	Thu May 15 00:14:15 2014 +0200
@@ -608,6 +608,16 @@ set_len(PyObject *so)
 }
 
 static int
+set_prealloc(PySetObject *so, Py_ssize_t length)
+{
+    if ((so->fill + length)*3 >= (so->mask+1)*2) {
+       if (set_table_resize(so, (so->used + length)*2) != 0)
+           return -1;
+    }
+    return 0;
+}
+
+static int
 set_merge(PySetObject *so, PyObject *otherset)
 {
     PySetObject *other;
@@ -627,10 +637,8 @@ set_merge(PySetObject *so, PyObject *oth
      * incrementally resizing as we insert new keys.  Expect
      * that there will be no (or few) overlapping keys.
      */
-    if ((so->fill + other->used)*3 >= (so->mask+1)*2) {
-       if (set_table_resize(so, (so->used + other->used)*2) != 0)
-           return -1;
-    }
+    if (set_prealloc(so, other->used) < 0)
+        return -1;
     for (i = 0; i <= other->mask; i++) {
         entry = &other->table[i];
         key = entry->key;
@@ -949,6 +957,7 @@ static int
 set_update_internal(PySetObject *so, PyObject *other)
 {
     PyObject *key, *it;
+    Py_ssize_t n;
 
     if (PyAnySet_Check(other))
         return set_merge(so, other);
@@ -965,10 +974,8 @@ set_update_internal(PySetObject *so, PyO
         */
         if (dictsize == -1)
             return -1;
-        if ((so->fill + dictsize)*3 >= (so->mask+1)*2) {
-            if (set_table_resize(so, (so->used + dictsize)*2) != 0)
-                return -1;
-        }
+        if (set_prealloc(so, dictsize) < 0)
+            return -1;
         while (_PyDict_Next(other, &pos, &key, &value, &hash)) {
             setentry an_entry;
 
@@ -984,6 +991,17 @@ set_update_internal(PySetObject *so, PyO
     if (it == NULL)
         return -1;
 
+    /* Guess a result set size. */
+    n = PyObject_LengthHint(other, PySet_MINSIZE);
+    if (n == -1) {
+        Py_DECREF(it);
+        return -1;
+    }
+    if (set_prealloc(so, n) < 0) {
+        Py_DECREF(it);
+        return -1;
+    }
+
     while ((key = PyIter_Next(it)) != NULL) {
         if (set_add_key(so, key) == -1) {
             Py_DECREF(it);