--- a/layout/generic/nsFrame.cpp
+++ b/layout/generic/nsFrame.cpp
@@ -1008,16 +1008,18 @@ nsFrame::DidSetStyleContext(nsStyleConte
   // bidi algorithm, we need to call |SetBidiEnabled| on the pres
   // context before reflow starts.  See bug 115921.
   if (StyleVisibility()->mDirection == NS_STYLE_DIRECTION_RTL) {
     PresContext()->SetBidiEnabled();
   }
 
   RemoveStateBits(NS_FRAME_SIMPLE_EVENT_REGIONS |
                   NS_FRAME_SIMPLE_DISPLAYLIST);
+
+  mMayHaveRoundedCorners = true;
 }
 
 void
 nsIFrame::ReparentFrameViewTo(nsViewManager* aViewManager,
                               nsView*        aNewParentView,
                               nsView*        aOldParentView)
 {
   if (HasView()) {
@@ -1582,32 +1584,40 @@ nsIFrame::OutsetBorderRadii(nscoord aRad
     }
   }
 }
 
 /* virtual */ bool
 nsIFrame::GetBorderRadii(const nsSize& aFrameSize, const nsSize& aBorderArea,
                          Sides aSkipSides, nscoord aRadii[8]) const
 {
+  if (!mMayHaveRoundedCorners) {
+    memset(aRadii, 0, sizeof(nscoord) * 8);
+    return false;
+  }
+
   if (IsThemed()) {
     // When we're themed, the native theme code draws the border and
     // background, and therefore it doesn't make sense to tell other
     // code that's interested in border-radius that we have any radii.
     //
     // In an ideal world, we might have a way for the them to tell us an
     // border radius, but since we don't, we're better off assuming
     // zero.
     NS_FOR_CSS_HALF_CORNERS(corner) {
       aRadii[corner] = 0;
     }
     return false;
   }
-  return ComputeBorderRadii(StyleBorder()->mBorderRadius,
-                            aFrameSize, aBorderArea,
-                            aSkipSides, aRadii);
+
+  const_cast<nsIFrame*>(this)->mMayHaveRoundedCorners =
+    ComputeBorderRadii(StyleBorder()->mBorderRadius,
+                       aFrameSize, aBorderArea,
+                       aSkipSides, aRadii);
+  return mMayHaveRoundedCorners;
 }
 
 bool
 nsIFrame::GetBorderRadii(nscoord aRadii[8]) const
 {
   nsSize sz = GetSize();
   return GetBorderRadii(sz, sz, GetSkipSides(), aRadii);
 }

--- a/layout/generic/nsIFrame.h
+++ b/layout/generic/nsIFrame.h
@@ -611,16 +611,17 @@ public:
     : mRect()
     , mContent(nullptr)
     , mStyleContext(nullptr)
     , mParent(nullptr)
     , mNextSibling(nullptr)
     , mPrevSibling(nullptr)
     , mState(NS_FRAME_FIRST_REFLOW | NS_FRAME_IS_DIRTY)
     , mClass(aID)
+    , mMayHaveRoundedCorners(false)
   {
     mozilla::PodZero(&mOverflow);
   }
 
   nsPresContext* PresContext() const {
     return StyleContext()->PresContext();
   }
 
@@ -3916,16 +3917,19 @@ protected:
   } mOverflow;
 
   /** @see GetWritingMode() */
   mozilla::WritingMode mWritingMode;
 
   /** The ClassID of the concrete class of this instance. */
   ClassID mClass; // 1 byte
 
+  bool mMayHaveRoundedCorners : 1;
+  // There should be a 15-bit gap left here.
+
   // Helpers
   /**
    * Can we stop inside this frame when we're skipping non-rendered whitespace?
    * @param  aForward [in] Are we moving forward (or backward) in content order.
    * @param  aOffset [in/out] At what offset into the frame to start looking.
    *         on output - what offset was reached (whether or not we found a place to stop).
    * @return STOP: An appropriate offset was found within this frame,
    *         and is given by aOffset.