diff --git a/packages/flutter/lib/src/rendering/shifted_box.dart b/packages/flutter/lib/src/rendering/shifted_box.dart
index f9a181aa9e..c9b74ac721 100644
--- a/packages/flutter/lib/src/rendering/shifted_box.dart
+++ b/packages/flutter/lib/src/rendering/shifted_box.dart
@@ -229,6 +229,9 @@ abstract class RenderAligningShiftedBox extends RenderShiftedBox {
   /// Initializes member variables for subclasses.
   ///
   /// The [alignment] argument must not be null.
+  ///
+  /// The [textDirection] must be non-null if the [alignment] is
+  /// direction-sensitive.
   RenderAligningShiftedBox({
     AlignmentGeometry alignment = Alignment.center,
     @required TextDirection textDirection,
@@ -303,6 +306,7 @@ abstract class RenderAligningShiftedBox extends RenderShiftedBox {
   ///
   /// This method must be called after the child has been laid out and
   /// this object's own size has been set.
+  @protected
   void alignChild() {
     _resolve();
     assert(child != null);
@@ -707,6 +711,9 @@ class RenderUnconstrainedBox extends RenderAligningShiftedBox with DebugOverflow
 /// A render object that is a specific size but passes its original constraints
 /// through to its child, which it allows to overflow.
 ///
+/// If the child's resulting size differs from this render object's size, then
+/// the child is aligned according to the [alignment] property.
+///
 /// See also:
 ///  * [RenderUnconstrainedBox] for a render object that allows its children
 ///    to render themselves unconstrained, expands to fit them, and considers
@@ -717,11 +724,14 @@ class RenderUnconstrainedBox extends RenderAligningShiftedBox with DebugOverflow
 class RenderSizedOverflowBox extends RenderAligningShiftedBox {
   /// Creates a render box of a given size that lets its child overflow.
   ///
-  /// The [requestedSize] argument must not be null.
+  /// The [requestedSize] and [alignment] arguments must not be null.
+  ///
+  /// The [textDirection] argument must not be null if the [alignment] is
+  /// direction-sensitive.
   RenderSizedOverflowBox({
     RenderBox child,
     @required Size requestedSize,
-    Alignment alignment = Alignment.center,
+    AlignmentGeometry alignment = Alignment.center,
     TextDirection textDirection,
   }) : assert(requestedSize != null),
        _requestedSize = requestedSize,
@@ -769,7 +779,7 @@ class RenderSizedOverflowBox extends RenderAligningShiftedBox {
   void performLayout() {
     size = constraints.constrain(_requestedSize);
     if (child != null) {
-      child.layout(constraints);
+      child.layout(constraints, parentUsesSize: true);
       alignChild();
     }
   }
@@ -783,17 +793,24 @@ class RenderSizedOverflowBox extends RenderAligningShiftedBox {
 /// for a given axis is null, then the constraints from the parent are just
 /// passed through instead.
 ///
-/// It then tries to size itself to the size of its child.
+/// It then tries to size itself to the size of its child. Where this is not
+/// possible (e.g. if the constraints from the parent are themselves tight), the
+/// child is aligned according to [alignment].
 class RenderFractionallySizedOverflowBox extends RenderAligningShiftedBox {
   /// Creates a render box that sizes its child to a fraction of the total available space.
   ///
   /// If non-null, the [widthFactor] and [heightFactor] arguments must be
   /// non-negative.
+  ///
+  /// The [alignment] must not be null.
+  ///
+  /// The [textDirection] must be non-null if the [alignment] is
+  /// direction-sensitive.
   RenderFractionallySizedOverflowBox({
     RenderBox child,
     double widthFactor,
     double heightFactor,
-    Alignment alignment = Alignment.center,
+    AlignmentGeometry alignment = Alignment.center,
     TextDirection textDirection,
   }) : _widthFactor = widthFactor,
        _heightFactor = heightFactor,
diff --git a/packages/flutter/test/widgets/fractionally_sized_box_test.dart b/packages/flutter/test/widgets/fractionally_sized_box_test.dart
index 2feb6b5046..006572e71c 100644
--- a/packages/flutter/test/widgets/fractionally_sized_box_test.dart
+++ b/packages/flutter/test/widgets/fractionally_sized_box_test.dart
@@ -29,4 +29,36 @@ void main() {
     expect(box.size, equals(const Size(50.0, 25.0)));
     expect(box.localToGlobal(Offset.zero), equals(const Offset(25.0, 37.5)));
   });
+
+  testWidgets('FractionallySizedBox alignment', (WidgetTester tester) async {
+    final GlobalKey inner = GlobalKey();
+    await tester.pumpWidget(Directionality(
+      textDirection: TextDirection.rtl,
+      child: FractionallySizedBox(
+        widthFactor: 0.5,
+        heightFactor: 0.5,
+        alignment: Alignment.topRight,
+        child: Placeholder(key: inner),
+      ),
+    ));
+    final RenderBox box = inner.currentContext.findRenderObject();
+    expect(box.size, equals(const Size(400.0, 300.0)));
+    expect(box.localToGlobal(box.size.center(Offset.zero)), equals(const Offset(800.0 - 400.0 / 2.0, 0.0 + 300.0 / 2.0)));
+  });
+
+  testWidgets('FractionallySizedBox alignment (direction-sensitive)', (WidgetTester tester) async {
+    final GlobalKey inner = GlobalKey();
+    await tester.pumpWidget(Directionality(
+      textDirection: TextDirection.rtl,
+      child: FractionallySizedBox(
+        widthFactor: 0.5,
+        heightFactor: 0.5,
+        alignment: AlignmentDirectional.topEnd,
+        child: Placeholder(key: inner),
+      ),
+    ));
+    final RenderBox box = inner.currentContext.findRenderObject();
+    expect(box.size, equals(const Size(400.0, 300.0)));
+    expect(box.localToGlobal(box.size.center(Offset.zero)), equals(const Offset(0.0 + 400.0 / 2.0, 0.0 + 300.0 / 2.0)));
+  });
 }
diff --git a/packages/flutter/test/widgets/overflow_box_test.dart b/packages/flutter/test/widgets/overflow_box_test.dart
index fbfb0fa2ae..e6c0517df5 100644
--- a/packages/flutter/test/widgets/overflow_box_test.dart
+++ b/packages/flutter/test/widgets/overflow_box_test.dart
@@ -49,4 +49,50 @@ void main() {
       'maxHeight: 4.0',
     ]);
   });
+
+  testWidgets('SizedOverflowBox alignment', (WidgetTester tester) async {
+    final GlobalKey inner = GlobalKey();
+    await tester.pumpWidget(Directionality(
+      textDirection: TextDirection.rtl,
+      child: Center(
+        child: SizedOverflowBox(
+          size: const Size(100.0, 100.0),
+          alignment: Alignment.topRight,
+          child: Container(height: 50.0, width: 50.0, key: inner),
+        ),
+      ),
+    ));
+    final RenderBox box = inner.currentContext.findRenderObject();
+    expect(box.size, equals(const Size(50.0, 50.0)));
+    expect(
+      box.localToGlobal(box.size.center(Offset.zero)),
+      equals(const Offset(
+        (800.0 - 100.0) / 2.0 + 100.0 - 50.0 / 2.0,
+        (600.0 - 100.0) / 2.0 + 0.0 + 50.0 / 2.0,
+      )),
+    );
+  });
+
+  testWidgets('SizedOverflowBox alignment (direction-sensitive)', (WidgetTester tester) async {
+    final GlobalKey inner = GlobalKey();
+    await tester.pumpWidget(Directionality(
+      textDirection: TextDirection.rtl,
+      child: Center(
+        child: SizedOverflowBox(
+          size: const Size(100.0, 100.0),
+          alignment: AlignmentDirectional.bottomStart,
+          child: Container(height: 50.0, width: 50.0, key: inner),
+        ),
+      ),
+    ));
+    final RenderBox box = inner.currentContext.findRenderObject();
+    expect(box.size, equals(const Size(50.0, 50.0)));
+    expect(
+      box.localToGlobal(box.size.center(Offset.zero)),
+      equals(const Offset(
+        (800.0 - 100.0) / 2.0 + 100.0 - 50.0 / 2.0,
+        (600.0 - 100.0) / 2.0 + 100.0 - 50.0 / 2.0,
+      )),
+    );
+  });
 }