diff --git a/editor/src/components/canvas/canvas-strategies/strategies/set-border-radius-strategy.spec.browser2.tsx b/editor/src/components/canvas/canvas-strategies/strategies/set-border-radius-strategy.spec.browser2.tsx
index 0794789c9b11..ac49bea9ee31 100644
--- a/editor/src/components/canvas/canvas-strategies/strategies/set-border-radius-strategy.spec.browser2.tsx
+++ b/editor/src/components/canvas/canvas-strategies/strategies/set-border-radius-strategy.spec.browser2.tsx
@@ -13,7 +13,6 @@ import { CanvasControlsContainerID } from '../../controls/new-canvas-controls'
 import { CircularHandleTestId } from '../../controls/select-mode/border-radius-control'
 import {
   mouseClickAtPoint,
-  mouseDoubleClickAtPoint,
   mouseDragFromPointToPoint,
   mouseDragFromPointWithDelta,
   mouseEnterAtPoint,
@@ -187,7 +186,8 @@ describe('set border radius strategy', () => {
       codeForDragTest(`borderTopLeftRadius: '24px',
                        borderTopRightRadius: '15px',
                        borderBottomRightRadius: '16px',
-                       borderBottomLeftRadius: '17px'`),
+                       borderBottomLeftRadius: '17px',
+                       overflow: 'hidden'`),
     )
   })
 
@@ -202,7 +202,7 @@ describe('set border radius strategy', () => {
 
     await doDragTest(editor, 'tl', 400, emptyModifiers)
     expect(getPrintedUiJsCode(editor.getEditorState())).toEqual(
-      codeForDragTest(`borderRadius: '${expectedBorderRadius}px'`),
+      codeForDragTest(`borderRadius: '${expectedBorderRadius}px', overflow: 'hidden'`),
     )
   })
 
@@ -213,7 +213,7 @@ describe('set border radius strategy', () => {
     )
     await doDragTest(editor, 'tl', -20, emptyModifiers)
     expect(getPrintedUiJsCode(editor.getEditorState())).toEqual(
-      codeForDragTest(`borderRadius: '0px'`),
+      codeForDragTest(`borderRadius: '0px', overflow: 'hidden'`),
     )
   })
 
@@ -240,7 +240,7 @@ describe('set border radius strategy', () => {
     await doDragTest(editor, 'tl', 400, emptyModifiers)
 
     expect(getPrintedUiJsCode(editor.getEditorState())).toEqual(
-      codeForDragTest(`borderRadius: '200px'`),
+      codeForDragTest(`borderRadius: '200px', overflow: 'hidden'`),
     )
 
     await resizeElement(
@@ -267,6 +267,7 @@ describe('set border radius strategy', () => {
               width: 300,
               height: 100,
               borderRadius: '40px',
+              overflow: 'hidden',
             }}
           />
         </div>`),
@@ -280,7 +281,7 @@ describe('set border radius strategy', () => {
     )
     await doDragTest(editor, 'tl', 10, emptyModifiers)
     expect(getPrintedUiJsCode(editor.getEditorState())).toEqual(
-      codeForDragTest(`borderRadius: '22px'`),
+      codeForDragTest(`borderRadius: '22px', overflow: 'hidden'`),
     )
   })
 
@@ -292,7 +293,7 @@ describe('set border radius strategy', () => {
       )
       await doDragTest(editor, 'tl', 10, emptyModifiers)
       expect(getPrintedUiJsCode(editor.getEditorState())).toEqual(
-        codeForDragTest(`borderRadius: '24px'`),
+        codeForDragTest(`borderRadius: '24px', overflow: 'hidden'`),
       )
     })
 
@@ -303,7 +304,7 @@ describe('set border radius strategy', () => {
       )
       await doDragTest(editor, 'tr', 10, emptyModifiers)
       expect(getPrintedUiJsCode(editor.getEditorState())).toEqual(
-        codeForDragTest(`borderRadius: '24px'`),
+        codeForDragTest(`borderRadius: '24px', overflow: 'hidden'`),
       )
     })
 
@@ -314,7 +315,7 @@ describe('set border radius strategy', () => {
       )
       await doDragTest(editor, 'bl', 10, emptyModifiers)
       expect(getPrintedUiJsCode(editor.getEditorState())).toEqual(
-        codeForDragTest(`borderRadius: '24px'`),
+        codeForDragTest(`borderRadius: '24px', overflow: 'hidden'`),
       )
     })
 
@@ -325,7 +326,7 @@ describe('set border radius strategy', () => {
       )
       await doDragTest(editor, 'br', 10, emptyModifiers)
       expect(getPrintedUiJsCode(editor.getEditorState())).toEqual(
-        codeForDragTest(`borderRadius: '24px'`),
+        codeForDragTest(`borderRadius: '24px', overflow: 'hidden'`),
       )
     })
   })
@@ -341,7 +342,8 @@ describe('set border radius strategy', () => {
         codeForDragTest(`borderTopLeftRadius: '24px',
                           borderTopRightRadius: '14px',
                           borderBottomRightRadius: '14px',
-                          borderBottomLeftRadius: '14px',`),
+                          borderBottomLeftRadius: '14px',
+                          overflow: 'hidden'`),
       )
     })
 
@@ -355,7 +357,8 @@ describe('set border radius strategy', () => {
         codeForDragTest(`borderTopLeftRadius: '14px',
                           borderTopRightRadius: '24px',
                           borderBottomRightRadius: '14px',
-                          borderBottomLeftRadius: '14px',`),
+                          borderBottomLeftRadius: '14px',
+                          overflow: 'hidden'`),
       )
     })
 
@@ -369,7 +372,8 @@ describe('set border radius strategy', () => {
         codeForDragTest(`borderTopLeftRadius: '14px',
                           borderTopRightRadius: '14px',
                           borderBottomRightRadius: '14px',
-                          borderBottomLeftRadius: '24px',`),
+                          borderBottomLeftRadius: '24px',
+                          overflow: 'hidden'`),
       )
     })
 
@@ -383,10 +387,43 @@ describe('set border radius strategy', () => {
         codeForDragTest(`borderTopLeftRadius: '14px',
                           borderTopRightRadius: '14px',
                           borderBottomRightRadius: '24px',
-                          borderBottomLeftRadius: '14px',`),
+                          borderBottomLeftRadius: '14px',
+                          overflow: 'hidden'`),
       )
     })
   })
+
+  describe('Overflow property handling', () => {
+    it('does not overwrite existing overflow property', async () => {
+      const editor = await renderTestEditorWithCode(
+        codeForDragTest(`borderRadius: '14px', overflow: 'visible',`),
+        'await-first-dom-report',
+      )
+      await doDragTest(editor, 'tl', 10, cmdModifier)
+      expect(getPrintedUiJsCode(editor.getEditorState())).toEqual(
+        codeForDragTest(`overflow: 'visible',
+                          borderTopLeftRadius: '24px',
+                          borderTopRightRadius: '14px',
+                          borderBottomRightRadius: '14px',
+                          borderBottomLeftRadius: '14px'`),
+      )
+    })
+
+    it('shows toast message', async () => {
+      const editor = await renderTestEditorWithCode(
+        codeForDragTest(`borderRadius: '14px',`),
+        'await-first-dom-report',
+      )
+      await doDragTest(editor, 'tl', 10, cmdModifier)
+      expect(editor.getEditorState().editor.toasts).toHaveLength(1)
+      expect(editor.getEditorState().editor.toasts[0]).toEqual({
+        id: 'property-added',
+        level: 'NOTICE',
+        message: 'Element now hides overflowing content',
+        persistent: false,
+      })
+    })
+  })
 })
 
 function codeForDragTest(borderRadius: string): string {
diff --git a/editor/src/components/canvas/canvas-strategies/strategies/set-border-radius-strategy.tsx b/editor/src/components/canvas/canvas-strategies/strategies/set-border-radius-strategy.tsx
index 4d0cd8a69430..b96b15eb4481 100644
--- a/editor/src/components/canvas/canvas-strategies/strategies/set-border-radius-strategy.tsx
+++ b/editor/src/components/canvas/canvas-strategies/strategies/set-border-radius-strategy.tsx
@@ -12,6 +12,7 @@ import {
   isJSXElement,
   jsxElementName,
   jsxElementNameEquals,
+  modifiableAttributeIsAttributeNotFound,
 } from '../../../../core/shared/element-template'
 import type { CanvasPoint, CanvasVector, Size } from '../../../../core/shared/math-utils'
 import {
@@ -69,6 +70,11 @@ import {
 import type { InteractionSession } from '../interaction-state'
 import { deleteProperties } from '../../commands/delete-properties-command'
 import { allElemsEqual } from '../../../../core/shared/array-utils'
+import * as PP from '../../../../core/shared/property-path'
+import { withUnderlyingTarget } from '../../../editor/store/editor-state'
+import type { ProjectContentTreeRoot } from '../../../assets'
+import { getModifiableJSXAttributeAtPath } from '../../../../core/shared/jsx-attributes'
+import { showToastCommand } from '../../commands/show-toast-command'
 
 export const SetBorderRadiusStrategyId = 'SET_BORDER_RADIUS_STRATEGY'
 
@@ -149,6 +155,7 @@ export const setBorderRadiusStrategy: CanvasStrategyFactory = (
       strategyApplicationResult([
         setCursorCommand(CSSCursor.Radius),
         ...commands(selectedElement),
+        ...getAddOverflowHiddenCommands(selectedElement, canvasState.projectContents),
         setElementsToRerenderCommand(selectedElements),
       ]),
   }
@@ -586,3 +593,30 @@ const setShorthandStylePropertyCommand =
       ]),
       setProperty('always', target, StyleProp('borderRadius'), value),
     ]
+
+function getAddOverflowHiddenCommands(
+  target: ElementPath,
+  projectContents: ProjectContentTreeRoot,
+): Array<CanvasCommand> {
+  const overflowProp = PP.create('style', 'overflow')
+
+  const propertyExists = withUnderlyingTarget(target, projectContents, false, (_, element) => {
+    if (isJSXElement(element)) {
+      return foldEither(
+        () => false,
+        (value) => !modifiableAttributeIsAttributeNotFound(value),
+        getModifiableJSXAttributeAtPath(element.props, overflowProp),
+      )
+    } else {
+      return false
+    }
+  })
+
+  if (propertyExists) {
+    return []
+  }
+  return [
+    showToastCommand('Element now hides overflowing content', 'NOTICE', 'property-added'),
+    setProperty('always', target, overflowProp, 'hidden'),
+  ]
+}