diff --git a/src/builtin_complete.cpp b/src/builtin_complete.cpp
index 934277477..de191d4d4 100644
--- a/src/builtin_complete.cpp
+++ b/src/builtin_complete.cpp
@@ -359,14 +359,8 @@ maybe_t<int> builtin_complete(parser_t &parser, io_streams_t &streams, wchar_t *
         parser.libdata().transient_commandlines.push_back(do_complete_param);
         cleanup_t remove_transient([&] { parser.libdata().transient_commandlines.pop_back(); });
 
-        if (parser.libdata().builtin_complete_current_commandline) {
-            // Prevent accidental recursion (see #6171).
-        } else if (parser.libdata().builtin_complete_recursion_level >= 24) {
-            // Allow a limited number of recursive calls to complete (#3474).
-            streams.err.append_format(L"%ls: maximum recursion depth reached\n", cmd);
-        } else {
-            parser.libdata().builtin_complete_recursion_level++;
-            assert(!parser.libdata().builtin_complete_current_commandline);
+        // Prevent accidental recursion (see #6171).
+        if (!parser.libdata().builtin_complete_current_commandline) {
             if (!have_do_complete_param)
                 parser.libdata().builtin_complete_current_commandline = true;
 
@@ -403,7 +397,6 @@ maybe_t<int> builtin_complete(parser_t &parser, io_streams_t &streams, wchar_t *
                 streams.out.push_back(L'\n');
             }
 
-            parser.libdata().builtin_complete_recursion_level--;
             parser.libdata().builtin_complete_current_commandline = false;
         }
     } else if (path.empty() && gnu_opt.empty()
diff --git a/src/complete.cpp b/src/complete.cpp
index 8b10f1df7..a7327c97c 100644
--- a/src/complete.cpp
+++ b/src/complete.cpp
@@ -1379,13 +1379,7 @@ void completer_t::complete_custom(const wcstring &cmd, const wcstring &cmdline,
         ctx.parser->libdata().transient_commandlines.push_back(unaliased_cmd);
         cleanup_t remove_transient(
             [&] { ctx.parser->libdata().transient_commandlines.pop_back(); });
-        // Prevent infinite recursion when the completion for x wraps "A=B x" (#7344).
-        // Don't report an error since this could be a legitimate alias.
-        static uint32_t complete_assignment_recursion_count;
-        if (complete_assignment_recursion_count++ < 24) {
-            run_on_command(std::move(unaliased_cmd));
-        }
-        complete_assignment_recursion_count--;
+        perform_for_command(std::move(unaliased_cmd));
         *do_file = false;
     } else if (!complete_param(cmd, previous_argument, current_argument,
                                !had_ddash)) {  // Invoke any custom completions for this command.
@@ -1511,6 +1505,21 @@ void completer_t::mark_completions_duplicating_arguments(const wcstring &cmd,
 }
 
 void completer_t::perform_for_command(wcstring cmd) {
+    // Limit recursion, in case a user-defined completion has cycles, or the completion for "x"
+    // wraps "A=B x" (#3474, #7344).  No need to do that when there is no parser: this happens only
+    // for autosuggestions where we don't evaluate command substitutions or variable assignments.
+    if (ctx.parser) {
+        if (ctx.parser->libdata().complete_recursion_level >= 24) {
+            debug(0, _(L"completion reached maximum recursion depth, possible cycle?"),
+                  cmd.c_str());
+            return;
+        }
+        ++ctx.parser->libdata().complete_recursion_level;
+    };
+    cleanup_t decrement{[this]() {
+        if (ctx.parser) --ctx.parser->libdata().complete_recursion_level;
+    }};
+
     const size_t cursor_pos = cmd.size();
 
     // Find the plain statement to operate on. The cursor may be past it (#1261), so backtrack
diff --git a/src/parser.h b/src/parser.h
index 7c8b37b01..aec1e934c 100644
--- a/src/parser.h
+++ b/src/parser.h
@@ -148,8 +148,8 @@ struct library_data_t {
     /// Last reader run count.
     uint64_t last_exec_run_counter{UINT64_MAX};
 
-    /// Number of recursive calls to builtin_complete().
-    uint32_t builtin_complete_recursion_level{0};
+    /// Number of recursive calls to the internal completion function.
+    uint32_t complete_recursion_level{0};
 
     /// If we're currently repainting the commandline.
     /// Useful to stop infinite loops.
diff --git a/tests/checks/complete.fish b/tests/checks/complete.fish
index e463490ed..7f5583a34 100644
--- a/tests/checks/complete.fish
+++ b/tests/checks/complete.fish
@@ -65,7 +65,7 @@ complete
 
 # Recursive calls to complete (see #3474)
 complete -c complete_test_recurse1 -xa '(echo recursing 1>&2; complete -C"complete_test_recurse1 ")'
-complete -C'complete_test_recurse1 '
+LANG=C complete -C'complete_test_recurse1 '
 # CHECKERR: recursing
 # CHECKERR: recursing
 # CHECKERR: recursing
@@ -90,7 +90,7 @@ complete -C'complete_test_recurse1 '
 # CHECKERR: recursing
 # CHECKERR: recursing
 # CHECKERR: recursing
-# CHECKERR: complete: maximum recursion depth reached
+# CHECKERR: <E> fish: completion reached maximum recursion depth, possible cycle?
 
 # short options
 complete -c foo -f -a non-option-argument
diff --git a/tests/checks/wraps.fish b/tests/checks/wraps.fish
index cd85051b3..98c014ba5 100644
--- a/tests/checks/wraps.fish
+++ b/tests/checks/wraps.fish
@@ -1,6 +1,8 @@
 #RUN: %fish %s
 # Validate some things about command wrapping.
 
+set -g LANG C # For predictable error messages.
+
 # This tests that we do not trigger a combinatorial explosion - see #5638.
 # Ensure it completes successfully.
 complete -c testcommand --wraps "testcommand x "
@@ -30,3 +32,4 @@ complete -C'testcommand2 explicit '
 
 complete -c recvar --wraps 'A=B recvar'
 complete -C 'recvar '
+# CHECKERR: <E> fish: completion reached maximum recursion depth, possible cycle?