diff --git a/doc/spec.md b/doc/spec.md
index ba5317a0..8711f0a2 100644
--- a/doc/spec.md
+++ b/doc/spec.md
@@ -3762,11 +3762,11 @@ x.symmetric_difference([3, 4, 5])         # set([1, 2, 4, 5])
 <a id='set·union'></a>
 ### set·union
 
-`S.union(iterable)` returns a new set into which have been inserted
-all the elements of set S and all the elements of the argument, which
-must be iterable.
+`S.union(iterable...)` returns a new set into which have been inserted
+all the elements of set S and each element of the iterable sequences.
 
-`union` fails if any element of the iterable is not hashable.
+`union` fails if any argument is not an iterable sequence, or if any
+sequence element is not hashable.
 
 ```python
 x = set([1, 2])
diff --git a/starlark/library.go b/starlark/library.go
index 10dfdfd1..6d7ff454 100644
--- a/starlark/library.go
+++ b/starlark/library.go
@@ -2337,41 +2337,18 @@ func set_symmetric_difference(_ *Thread, b *Builtin, args Tuple, kwargs []Tuple)
 
 // https://github.com/google/starlark-go/blob/master/doc/spec.md#set·union.
 func set_union(_ *Thread, b *Builtin, args Tuple, kwargs []Tuple) (Value, error) {
-	var iterable Iterable
-	if err := UnpackPositionalArgs(b.Name(), args, kwargs, 0, &iterable); err != nil {
-		return nil, err
-	}
-	iter := iterable.Iterate()
-	defer iter.Done()
-	union, err := b.Receiver().(*Set).Union(iter)
-	if err != nil {
+	receiverSet := b.Receiver().(*Set).clone()
+	if err := setUpdate(receiverSet, args, kwargs); err != nil {
 		return nil, nameErr(b, err)
 	}
-	return union, nil
+	return receiverSet, nil
 }
 
 // https://github.com/google/starlark-go/blob/master/doc/spec.md#set·update.
 func set_update(_ *Thread, b *Builtin, args Tuple, kwargs []Tuple) (Value, error) {
-	if len(kwargs) > 0 {
-		return nil, nameErr(b, "update does not accept keyword arguments")
-	}
-
-	receiverSet := b.Receiver().(*Set)
-
-	for i, arg := range args {
-		iterable, ok := arg.(Iterable)
-		if !ok {
-			return nil, fmt.Errorf("update: argument #%d is not iterable: %s", i+1, arg.Type())
-		}
-		if err := func() error {
-			iter := iterable.Iterate()
-			defer iter.Done()
-			return receiverSet.InsertAll(iter)
-		}(); err != nil {
-			return nil, nameErr(b, err)
-		}
+	if err := setUpdate(b.Receiver().(*Set), args, kwargs); err != nil {
+		return nil, nameErr(b, err)
 	}
-
 	return None, nil
 }
 
@@ -2474,6 +2451,28 @@ func updateDict(dict *Dict, updates Tuple, kwargs []Tuple) error {
 	return nil
 }
 
+func setUpdate(s *Set, args Tuple, kwargs []Tuple) error {
+	if len(kwargs) > 0 {
+		return errors.New("does not accept keyword arguments")
+	}
+
+	for i, arg := range args {
+		iterable, ok := arg.(Iterable)
+		if !ok {
+			return fmt.Errorf("argument #%d is not iterable: %s", i+1, arg.Type())
+		}
+		if err := func() error {
+			iter := iterable.Iterate()
+			defer iter.Done()
+			return s.InsertAll(iter)
+		}(); err != nil {
+			return err
+		}
+	}
+
+	return nil
+}
+
 // nameErr returns an error message of the form "name: msg"
 // where name is b.Name() and msg is a string or error.
 func nameErr(b *Builtin, msg interface{}) error {
diff --git a/starlark/testdata/set.star b/starlark/testdata/set.star
index 7a831129..9aa722b1 100644
--- a/starlark/testdata/set.star
+++ b/starlark/testdata/set.star
@@ -59,14 +59,23 @@ assert.eq(list(set("a".elems()).union("b".elems())), ["a", "b"])
 assert.eq(list(set("ab".elems()).union("bc".elems())), ["a", "b", "c"])
 assert.eq(set().union([]), set())
 assert.eq(type(x.union(y)), "set")
+assert.eq(list(x.union()), [1, 2, 3])
 assert.eq(list(x.union(y)), [1, 2, 3, 4, 5])
+assert.eq(list(x.union(y, [6, 7])), [1, 2, 3, 4, 5, 6, 7])
 assert.eq(list(x.union([5, 1])), [1, 2, 3, 5])
 assert.eq(list(x.union((6, 5, 4))), [1, 2, 3, 6, 5, 4])
 assert.fails(lambda : x.union([1, 2, {}]), "unhashable type: dict")
+assert.fails(lambda : x.union(1, 2, 3), "argument #1 is not iterable: int")
 
 # set.update (allows any iterable for the right operand)
 # The update function will mutate the set so the tests below are
 # scoped using a function.
+
+def test_update_return_value():
+    assert.eq(set(x).update(y), None)
+
+test_update_return_value()
+
 def test_update_elems_singular():
     s = set("a".elems())
     s.update("b".elems())
@@ -130,7 +139,7 @@ test_update_non_iterable()
 
 def test_update_kwargs():
     s = set(x)
-    assert.fails(lambda: x.update(gee = [3, 4]), "update: update does not accept keyword arguments")
+    assert.fails(lambda: x.update(gee = [3, 4]), "update: does not accept keyword arguments")
 
 test_update_kwargs()