bool defaultNoEscape = isFunctionParam;
 
-  // Desugar here
-  auto *funcTy = ty->castTo<FunctionType>();
+  // Partial desugaring means that desugaring stops once we find the type we want
+  auto *funcTy = ty->partialDesugarCastTo<FunctionType>();
   auto extInfo = funcTy->getExtInfo();
   if (defaultNoEscape && !extInfo.isNoEscape()) {
     extInfo = extInfo.withNoEscape();
 
-    // We lost the sugar to flip the isNoEscape bit.
-    //
-    // FIXME: It would be better to add a new AttributedType sugared type,
-    // which would wrap the NameAliasType or ParenType, and apply the
-    // isNoEscape bit when de-sugaring.
-    // <https://bugs.swift.org/browse/SR-2520>
-    return FunctionType::get(funcTy->getInput(), funcTy->getResult(), extInfo);
+    auto newTy = FunctionType::get(funcTy->getInput(), funcTy->getResult(), extInfo);
+    return ty->rebuildSugar(/*orig*/funcTy, /*replacement*/newTy);
   }
 
   // Note: original sugared type
   return ty;