diff --git a/include/fmt/compile.h b/include/fmt/compile.h
index 3036b6a6..6555fd78 100644
--- a/include/fmt/compile.h
+++ b/include/fmt/compile.h
@@ -348,22 +348,18 @@ constexpr parse_specs_result<T, Char> parse_specs(basic_string_view<Char> str,
 template <typename Char> struct arg_id_handler {
   arg_ref<Char> arg_id;
 
-  constexpr int operator()() {
+  constexpr int on_auto() {
     FMT_ASSERT(false, "handler cannot be used with automatic indexing");
     return 0;
   }
-  constexpr int operator()(int id) {
+  constexpr int on_index(int id) {
     arg_id = arg_ref<Char>(id);
     return 0;
   }
-  constexpr int operator()(basic_string_view<Char> id) {
+  constexpr int on_name(basic_string_view<Char> id) {
     arg_id = arg_ref<Char>(id);
     return 0;
   }
-
-  constexpr void on_error(const char* message) {
-    FMT_THROW(format_error(message));
-  }
 };
 
 template <typename Char> struct parse_arg_id_result {
diff --git a/include/fmt/core.h b/include/fmt/core.h
index d0534730..cc5f443f 100644
--- a/include/fmt/core.h
+++ b/include/fmt/core.h
@@ -2425,20 +2425,20 @@ FMT_CONSTEXPR auto do_parse_arg_id(const Char* begin, const Char* end,
     else
       ++begin;
     if (begin == end || (*begin != '}' && *begin != ':'))
-      handler.on_error("invalid format string");
+      throw_format_error("invalid format string");
     else
-      handler(index);
+      handler.on_index(index);
     return begin;
   }
   if (!is_name_start(c)) {
-    handler.on_error("invalid format string");
+    throw_format_error("invalid format string");
     return begin;
   }
   auto it = begin;
   do {
     ++it;
-  } while (it != end && (is_name_start(c = *it) || ('0' <= c && c <= '9')));
-  handler(basic_string_view<Char>(begin, to_unsigned(it - begin)));
+  } while (it != end && (is_name_start(*it) || ('0' <= *it && *it <= '9')));
+  handler.on_name({begin, to_unsigned(it - begin)});
   return it;
 }
 
@@ -2447,7 +2447,7 @@ FMT_CONSTEXPR FMT_INLINE auto parse_arg_id(const Char* begin, const Char* end,
                                            IDHandler&& handler) -> const Char* {
   Char c = *begin;
   if (c != '}' && c != ':') return do_parse_arg_id(begin, end, handler);
-  handler();
+  handler.on_auto();
   return begin;
 }
 
@@ -2455,25 +2455,22 @@ template <typename Char> struct dynamic_spec_id_handler {
   basic_format_parse_context<Char>& ctx;
   dynamic_spec<Char> spec;
 
-  FMT_CONSTEXPR void operator()() {
+  FMT_CONSTEXPR void on_auto() {
     spec.kind = dynamic_spec_kind::index;
     spec.value = ctx.next_arg_id();
     ctx.check_dynamic_spec(spec.value);
   }
-  FMT_CONSTEXPR void operator()(int id) {
+  FMT_CONSTEXPR void on_index(int id) {
     spec.kind = dynamic_spec_kind::index;
     spec.value = id;
     ctx.check_arg_id(id);
     ctx.check_dynamic_spec(id);
   }
-  FMT_CONSTEXPR void operator()(basic_string_view<Char> id) {
+  FMT_CONSTEXPR void on_name(basic_string_view<Char> id) {
     spec.kind = dynamic_spec_kind::name;
     spec.name = id;
     ctx.check_arg_id(id);
   }
-  FMT_CONSTEXPR void on_error(const char* message) {
-    if (message) throw_format_error("invalid format string");
-  }
 };
 
 template <typename Char> struct parse_dynamic_spec_result {
@@ -2654,14 +2651,11 @@ FMT_CONSTEXPR auto parse_replacement_field(const Char* begin, const Char* end,
     Handler& handler;
     int arg_id;
 
-    FMT_CONSTEXPR void operator()() { arg_id = handler.on_arg_id(); }
-    FMT_CONSTEXPR void operator()(int id) { arg_id = handler.on_arg_id(id); }
-    FMT_CONSTEXPR void operator()(basic_string_view<Char> id) {
+    FMT_CONSTEXPR void on_auto() { arg_id = handler.on_arg_id(); }
+    FMT_CONSTEXPR void on_index(int id) { arg_id = handler.on_arg_id(id); }
+    FMT_CONSTEXPR void on_name(basic_string_view<Char> id) {
       arg_id = handler.on_arg_id(id);
     }
-    FMT_CONSTEXPR void on_error(const char* message) {
-      if (message) handler.on_error(message);
-    }
   };
 
   ++begin;
diff --git a/test/core-test.cc b/test/core-test.cc
index 55f7fb0b..fb833bd2 100644
--- a/test/core-test.cc
+++ b/test/core-test.cc
@@ -485,30 +485,28 @@ TEST(arg_test, visit_invalid_arg) {
 
 #if FMT_USE_CONSTEXPR
 
-enum class arg_id_result { none, empty, index, name, error };
+enum class arg_id_result { none, empty, index, name };
 struct test_arg_id_handler {
   arg_id_result res = arg_id_result::none;
   int index = 0;
   string_view name;
 
-  constexpr void operator()() { res = arg_id_result::empty; }
+  constexpr void on_auto() { res = arg_id_result::empty; }
 
-  constexpr void operator()(int i) {
+  constexpr void on_index(int i) {
     res = arg_id_result::index;
     index = i;
   }
 
-  constexpr void operator()(string_view n) {
+  constexpr void on_name(string_view n) {
     res = arg_id_result::name;
     name = n;
   }
-
-  constexpr void on_error(const char*) { res = arg_id_result::error; }
 };
 
 template <size_t N>
 constexpr test_arg_id_handler parse_arg_id(const char (&s)[N]) {
-  test_arg_id_handler h;
+  auto h = test_arg_id_handler();
   fmt::detail::parse_arg_id(s, s + N, h);
   return h;
 }
@@ -520,7 +518,6 @@ TEST(format_test, constexpr_parse_arg_id) {
   static_assert(parse_arg_id("42:").index == 42, "");
   static_assert(parse_arg_id("foo:").res == arg_id_result::name, "");
   static_assert(parse_arg_id("foo:").name.size() == 3, "");
-  static_assert(parse_arg_id("!").res == arg_id_result::error, "");
 }
 
 struct test_format_specs_handler {