diff --git a/src/builtin_complete.cpp b/src/builtin_complete.cpp
index 7a7faa8ed..ef4ae8b88 100644
--- a/src/builtin_complete.cpp
+++ b/src/builtin_complete.cpp
@@ -336,7 +336,10 @@ int builtin_complete(parser_t &parser, io_streams_t &streams, wchar_t **argv) {
         parser.libdata().transient_commandlines.push_back(do_complete_param);
         cleanup_t remove_transient([&] { parser.libdata().transient_commandlines.pop_back(); });
 
-        if (parser.libdata().builtin_complete_recursion_level < 1) {
+        // Allow a limited number of recursive calls to complete (#3474).
+        if (parser.libdata().builtin_complete_recursion_level >= 1) {
+            streams.err.append_format(L"%ls: maximum recursive depth reached\n", cmd);
+        } else {
             parser.libdata().builtin_complete_recursion_level++;
 
             std::vector<completion_t> comp;
diff --git a/tests/checks/complete.fish b/tests/checks/complete.fish
index a232fb589..733f78c3a 100644
--- a/tests/checks/complete.fish
+++ b/tests/checks/complete.fish
@@ -59,3 +59,9 @@ complete
 # CHECK: complete {{.*}}
 # CHECK: complete {{.*}}
 # CHECK: 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 '
+# CHECKERR: recursing
+# CHECKERR: complete: maximum recursive depth reached
diff --git a/tests/checks/wraps.fish b/tests/checks/wraps.fish
index 5ffc9edb5..14d223977 100644
--- a/tests/checks/wraps.fish
+++ b/tests/checks/wraps.fish
@@ -26,4 +26,6 @@ complete -c testcommand2 -x -a "(testcommand2_complete)"
 complete -c testcommand2 --wraps "testcommand2 from_wraps "
 complete -C'testcommand2 explicit '
 # CHECKERR: explicit
+# CHECKERR: complete: maximum recursive depth reached
 # CHECKERR: from_wraps explicit
+# CHECKERR: complete: maximum recursive depth reached