diff --git a/packages/flutter/lib/src/material/popup_menu.dart b/packages/flutter/lib/src/material/popup_menu.dart
index 0f7732ca048..78b1e9ec338 100644
--- a/packages/flutter/lib/src/material/popup_menu.dart
+++ b/packages/flutter/lib/src/material/popup_menu.dart
@@ -435,7 +435,6 @@ class PopupMenuItemState<T, W extends PopupMenuItem<T>> extends State<W> {
       child: ConstrainedBox(
         constraints: BoxConstraints(minHeight: widget.height),
         child: Padding(
-          key: const Key('menu item padding'),
           padding: padding,
           child: Align(alignment: AlignmentDirectional.centerStart, child: buildChild()),
         ),
diff --git a/packages/flutter/lib/src/material/time_picker.dart b/packages/flutter/lib/src/material/time_picker.dart
index 99916e2f6ac..e8fc0464da1 100644
--- a/packages/flutter/lib/src/material/time_picker.dart
+++ b/packages/flutter/lib/src/material/time_picker.dart
@@ -1615,7 +1615,7 @@ class _DialState extends State<_Dial> with SingleTickerProviderStateMixin {
       onPanUpdate: _handlePanUpdate,
       onPanEnd: _handlePanEnd,
       onTapUp: _handleTapUp,
-      child: CustomPaint(key: const ValueKey<String>('time-picker-dial'), painter: painter),
+      child: CustomPaint(painter: painter),
     );
   }
 }
diff --git a/packages/flutter/test/material/popup_menu_test.dart b/packages/flutter/test/material/popup_menu_test.dart
index 85f6c7987f5..a1f175af233 100644
--- a/packages/flutter/test/material/popup_menu_test.dart
+++ b/packages/flutter/test/material/popup_menu_test.dart
@@ -1756,14 +1756,7 @@ void main() {
     await tester.pumpAndSettle();
 
     EdgeInsetsGeometry paddingFor(String text) {
-      return tester
-          .widget<Padding>(
-            find.ancestor(
-              of: find.widgetWithText(Align, 'Item 0'),
-              matching: find.byKey(const Key('menu item padding')),
-            ),
-          )
-          .padding;
+      return tester.widget<Padding>(find.widgetWithText(Padding, 'Item 0').first).padding;
     }
 
     expect(paddingFor('Item 0'), const EdgeInsets.symmetric(horizontal: 12.0));
@@ -1831,14 +1824,7 @@ void main() {
     await tester.pumpAndSettle();
 
     EdgeInsetsGeometry paddingFor(String text) {
-      return tester
-          .widget<Padding>(
-            find.ancestor(
-              of: find.widgetWithText(Align, 'Item 0'),
-              matching: find.byKey(const Key('menu item padding')),
-            ),
-          )
-          .padding;
+      return tester.widget<Padding>(find.widgetWithText(Padding, 'Item 0').first).padding;
     }
 
     expect(paddingFor('Item 0'), const EdgeInsets.symmetric(horizontal: 16.0));
diff --git a/packages/flutter/test/material/time_picker_test.dart b/packages/flutter/test/material/time_picker_test.dart
index dce54c23b53..6f2423d6974 100644
--- a/packages/flutter/test/material/time_picker_test.dart
+++ b/packages/flutter/test/material/time_picker_test.dart
@@ -2653,9 +2653,11 @@ Future<Offset?> startPicker(
   );
   await tester.tap(find.text('X'));
   await tester.pumpAndSettle(const Duration(seconds: 1));
-  return entryMode == TimePickerEntryMode.dial
-      ? tester.getCenter(find.byKey(const ValueKey<String>('time-picker-dial')))
-      : null;
+  final Finder customPaintFinder = find.descendant(
+    of: find.byWidgetPredicate((Widget w) => '${w.runtimeType}' == '_Dial'),
+    matching: find.byType(CustomPaint),
+  );
+  return entryMode == TimePickerEntryMode.dial ? tester.getCenter(customPaintFinder) : null;
 }
 
 Future<void> finishPicker(WidgetTester tester) async {
diff --git a/packages/flutter/test/painting/system_fonts_test.dart b/packages/flutter/test/painting/system_fonts_test.dart
index cfd19db4c4c..7985fe9432c 100644
--- a/packages/flutter/test/painting/system_fonts_test.dart
+++ b/packages/flutter/test/painting/system_fonts_test.dart
@@ -257,12 +257,11 @@ void main() {
       SystemChannels.system.codec.encodeMessage(data),
       (ByteData? data) {},
     );
-    final RenderObject renderObject = tester.renderObject(
-      find.descendant(
-        of: find.byKey(const Key('parent')),
-        matching: find.byKey(const ValueKey<String>('time-picker-dial')),
-      ),
+    final Finder customPaintFinder = find.descendant(
+      of: find.byWidgetPredicate((Widget w) => '${w.runtimeType}' == '_Dial'),
+      matching: find.byType(CustomPaint),
     );
+    final RenderObject renderObject = tester.renderObject(customPaintFinder);
     expect(renderObject.debugNeedsPaint, isTrue);
   });
 }
diff --git a/packages/flutter_localizations/test/material/time_picker_test.dart b/packages/flutter_localizations/test/material/time_picker_test.dart
index da831930261..b233404e780 100644
--- a/packages/flutter_localizations/test/material/time_picker_test.dart
+++ b/packages/flutter_localizations/test/material/time_picker_test.dart
@@ -6,6 +6,11 @@ import 'package:flutter/material.dart';
 import 'package:flutter_localizations/flutter_localizations.dart';
 import 'package:flutter_test/flutter_test.dart';
 
+final Finder dialCustomPaintFinder = find.descendant(
+  of: find.byWidgetPredicate((Widget w) => '${w.runtimeType}' == '_Dial'),
+  matching: find.byType(CustomPaint),
+);
+
 void main() {
   testWidgets('Material2 - can localize the header in all known formats - portrait', (
     WidgetTester tester,
@@ -567,7 +572,7 @@ void main() {
           locale: locale,
           useMaterial3: false,
         );
-        final Size size = tester.getSize(find.byKey(const Key('time-picker-dial')));
+        final Size size = tester.getSize(dialCustomPaintFinder);
         final double dy = (size.height / 2.0 / 10) * i;
         await tester.tapAt(Offset(center.dx, center.dy - dy));
         await finishPicker(tester);
@@ -598,7 +603,7 @@ void main() {
           locale: locale,
           useMaterial3: true,
         );
-        final Size size = tester.getSize(find.byKey(const Key('time-picker-dial')));
+        final Size size = tester.getSize(dialCustomPaintFinder);
         final double dy = (size.height / 2.0 / 10) * factor;
         await tester.tapAt(Offset(center.dx, center.dy - dy));
         await finishPicker(tester);
@@ -740,9 +745,7 @@ void main() {
   ) async {
     await mediaQueryBoilerplate(tester, alwaysUse24HourFormat: false, useMaterial3: false);
 
-    final CustomPaint dialPaint = tester.widget(
-      find.byKey(const ValueKey<String>('time-picker-dial')),
-    );
+    final CustomPaint dialPaint = tester.widget(dialCustomPaintFinder);
     final dynamic dialPainter = dialPaint.painter;
     // ignore: avoid_dynamic_calls
     final List<dynamic> primaryLabels = dialPainter.primaryLabels as List<dynamic>;
@@ -770,9 +773,7 @@ void main() {
   ) async {
     await mediaQueryBoilerplate(tester, alwaysUse24HourFormat: false, useMaterial3: true);
 
-    final CustomPaint dialPaint = tester.widget(
-      find.byKey(const ValueKey<String>('time-picker-dial')),
-    );
+    final CustomPaint dialPaint = tester.widget(dialCustomPaintFinder);
     final dynamic dialPainter = dialPaint.painter;
     // ignore: avoid_dynamic_calls
     final List<dynamic> primaryLabels = dialPainter.primaryLabels as List<dynamic>;
@@ -800,9 +801,7 @@ void main() {
   ) async {
     await mediaQueryBoilerplate(tester, alwaysUse24HourFormat: true, useMaterial3: true);
 
-    final CustomPaint dialPaint = tester.widget(
-      find.byKey(const ValueKey<String>('time-picker-dial')),
-    );
+    final CustomPaint dialPaint = tester.widget(dialCustomPaintFinder);
     final dynamic dialPainter = dialPaint.painter;
     // ignore: avoid_dynamic_calls
     final List<dynamic> primaryLabels = dialPainter.primaryLabels as List<dynamic>;
@@ -830,9 +829,7 @@ void main() {
   ) async {
     await mediaQueryBoilerplate(tester, alwaysUse24HourFormat: true, useMaterial3: false);
 
-    final CustomPaint dialPaint = tester.widget(
-      find.byKey(const ValueKey<String>('time-picker-dial')),
-    );
+    final CustomPaint dialPaint = tester.widget(dialCustomPaintFinder);
     final dynamic dialPainter = dialPaint.painter;
     // ignore: avoid_dynamic_calls
     final List<dynamic> primaryLabels = dialPainter.primaryLabels as List<dynamic>;
@@ -968,7 +965,7 @@ Future<Offset> startPicker(
   );
   await tester.tap(find.text('X'));
   await tester.pumpAndSettle(const Duration(seconds: 1));
-  return tester.getCenter(find.byKey(const Key('time-picker-dial')));
+  return tester.getCenter(dialCustomPaintFinder);
 }
 
 Future<void> finishPicker(WidgetTester tester) async {