diff --git a/doc/variant2/reference.adoc b/doc/variant2/reference.adoc
index 5748989..897fbf4 100644
--- a/doc/variant2/reference.adoc
+++ b/doc/variant2/reference.adoc
@@ -151,8 +151,8 @@ template<class R = /*unspecified*/, class F, class... V>
 
 // visit_by_index (extension)
 
-template<class V, class... F>
-  void visit_by_index(V&& v, F&&.. f);
+template<class R = /*unspecified*/, class V, class... F>
+  constexpr /*see below*/ visit_by_index(V&& v, F&&.. f);
 
 // monostate
 
@@ -899,16 +899,20 @@ Remarks: :: If `R` is given explicitly, as in `visit<int>`, the return
 ### visit_by_index (extension)
 
 ```
-template<class V, class... F>
-  void visit_by_index(V&& v, F&&.. f);
+template<class R = /*unspecified*/, class V, class... F>
+  constexpr /*see below*/ visit_by_index(V&& v, F&&.. f);
 ```
 [none]
 * {blank}
 +
 Requires: :: `variant_size<V>::value == sizeof...(F)`, or the program is ill-formed.
-Effects: :: `std::forward<Fi>(fi)(get<i>(std::forward<V>(v)))`, where
+Returns: :: `std::forward<Fi>(fi)(get<i>(std::forward<V>(v)))`, where
   `i` is `v.index()` and `Fi` and `fi` are the `i`-th element of `F...` and `f...`
   accordingly.
+Remarks: :: If `R` is given explicitly, as in `visit_by_index<int>`, the return
+  type is `R`. Otherwise, it's deduced from `F...` and `V`. All the applications
+  of `Fi` to the corresponding variant alternatives must have the same return type
+  for this deduction to succeed.
 
 ### swap