diff --git a/DOCS/man/lua.rst b/DOCS/man/lua.rst
index 2900a5393c..5da358a12c 100644
--- a/DOCS/man/lua.rst
+++ b/DOCS/man/lua.rst
@@ -240,7 +240,9 @@ The ``mp`` module is preloaded, although it can be loaded manually with
     an example). The name should be unique across other bindings in the same
     script - if not, the previous binding with the same name will be
     overwritten. You can omit the name, in which case a random name is generated
-    internally.
+    internally. (Omitting works as follows: either pass ``nil`` for ``name``,
+    or pass the ``fn`` argument in place of the name. The latter is not
+    recommended and is handled for compatibility only.)
 
     The last argument is used for optional flags. This is a table, which can
     have the following entries:
diff --git a/player/lua/defaults.lua b/player/lua/defaults.lua
index 38b6a9d04b..72b73b566b 100644
--- a/player/lua/defaults.lua
+++ b/player/lua/defaults.lua
@@ -157,8 +157,12 @@ end
 
 local function add_binding(attrs, key, name, fn, rp)
     rp = rp or ""
-    if (type(name) ~= "string") and (not fn) then
+    if (type(name) ~= "string") and (name ~= nil) then
+        rp = fn
         fn = name
+        name = nil
+    end
+    if name == nil then
         name = reserve_binding()
     end
     local repeatable = rp == "repeatable" or rp["repeatable"]