diff --git a/common/json-schema-to-grammar.cpp b/common/json-schema-to-grammar.cpp
index 58f3c2ae9..716801b5c 100644
--- a/common/json-schema-to-grammar.cpp
+++ b/common/json-schema-to-grammar.cpp
@@ -452,15 +452,11 @@ private:
                 }
                 std::string k = ks[0];
                 std::string kv_rule_name = prop_kv_rule_names[k];
-                if (k == "*") {
-                    res = _add_rule(
-                        name + (name.empty() ? "" : "-") + "additional-kvs",
-                        kv_rule_name + " ( \",\" space " + kv_rule_name + " )*"
-                    );
-                } else if (first_is_optional) {
-                    res = "( \",\" space " + kv_rule_name + " )?";
+                std::string comma_ref = "( \",\" space " + kv_rule_name + " )";
+                if (first_is_optional) {
+                    res = comma_ref + (k == "*" ? "*" : "?");
                 } else {
-                    res = kv_rule_name;
+                    res = kv_rule_name + (k == "*" ? " " + comma_ref + "*" : "");
                 }
                 if (ks.size() > 1) {
                     res += " " + _add_rule(
diff --git a/examples/json_schema_to_grammar.py b/examples/json_schema_to_grammar.py
index 15631d53c..65ce2d364 100755
--- a/examples/json_schema_to_grammar.py
+++ b/examples/json_schema_to_grammar.py
@@ -489,15 +489,11 @@ class SchemaConverter:
             def get_recursive_refs(ks, first_is_optional):
                 [k, *rest] = ks
                 kv_rule_name = prop_kv_rule_names[k]
-                if k == '*':
-                    res = self._add_rule(
-                        f'{name}{"-" if name else ""}additional-kvs',
-                        f'{kv_rule_name} ( "," space ' + kv_rule_name + ' )*'
-                    )
-                elif first_is_optional:
-                    res = f'( "," space {kv_rule_name} )?'
+                comma_ref = f'( "," space {kv_rule_name} )'
+                if first_is_optional:
+                    res = comma_ref + ('*' if k == '*' else '?')
                 else:
-                    res = kv_rule_name
+                    res = kv_rule_name + (' ' + comma_ref + "*" if k == '*' else '')
                 if len(rest) > 0:
                     res += ' ' + self._add_rule(
                         f'{name}{"-" if name else ""}{k}-rest',
diff --git a/examples/server/public/json-schema-to-grammar.mjs b/examples/server/public/json-schema-to-grammar.mjs
index ded37c981..842659bf8 100644
--- a/examples/server/public/json-schema-to-grammar.mjs
+++ b/examples/server/public/json-schema-to-grammar.mjs
@@ -506,15 +506,11 @@ export class SchemaConverter {
         const [k, ...rest] = ks;
         const kvRuleName = propKvRuleNames[k];
         let res;
-        if (k === '*') {
-            res = this._addRule(
-                `${name ?? ''}${name ? '-' : ''}additional-kvs`,
-                `${kvRuleName} ( "," space ` + kvRuleName + ` )*`
-            )
-        } else if (firstIsOptional) {
-          res = `( "," space ${kvRuleName} )?`;
+        const commaRef = `( "," space ${kvRuleName} )`;
+        if (firstIsOptional) {
+          res = commaRef + (k === '*' ? '*' : '?');
         } else {
-          res = kvRuleName;
+          res = kvRuleName + (k === '*' ? ' ' + commaRef + '*' : '');
         }
         if (rest.length > 0) {
           res += ' ' + this._addRule(
diff --git a/tests/test-json-schema-to-grammar.cpp b/tests/test-json-schema-to-grammar.cpp
index 780e1932a..478a2e2e9 100755
--- a/tests/test-json-schema-to-grammar.cpp
+++ b/tests/test-json-schema-to-grammar.cpp
@@ -552,13 +552,12 @@ static void test_all(const std::string & lang, std::function<void(const TestCase
         })""",
         R"""(
             additional-kv ::= string ":" space additional-value
-            additional-kvs ::= additional-kv ( "," space additional-kv )*
             additional-value ::= "[" space (number ("," space number)*)? "]" space
             char ::= [^"\\] | "\\" (["\\/bfnrt] | "u" [0-9a-fA-F]{4})
             decimal-part ::= [0-9]{1,16}
             integral-part ::= [0] | [1-9] [0-9]{0,15}
             number ::= ("-"? integral-part) ("." decimal-part)? ([eE] [-+]? integral-part)? space
-            root ::= "{" space  (additional-kvs )? "}" space
+            root ::= "{" space  (additional-kv ( "," space additional-kv )* )? "}" space
             space ::= " "?
             string ::= "\"" char* "\"" space
         )"""
@@ -636,12 +635,11 @@ static void test_all(const std::string & lang, std::function<void(const TestCase
         R"""(
             a-kv ::= "\"a\"" space ":" space number
             additional-kv ::= string ":" space string
-            additional-kvs ::= additional-kv ( "," space additional-kv )*
             char ::= [^"\\] | "\\" (["\\/bfnrt] | "u" [0-9a-fA-F]{4})
             decimal-part ::= [0-9]{1,16}
             integral-part ::= [0] | [1-9] [0-9]{0,15}
             number ::= ("-"? integral-part) ("." decimal-part)? ([eE] [-+]? integral-part)? space
-            root ::= "{" space a-kv ( "," space ( additional-kvs ) )? "}" space
+            root ::= "{" space a-kv ( "," space ( additional-kv ( "," space additional-kv )* ) )? "}" space
             space ::= " "?
             string ::= "\"" char* "\"" space
         )"""
@@ -659,14 +657,13 @@ static void test_all(const std::string & lang, std::function<void(const TestCase
         })""",
         R"""(
             a-kv ::= "\"a\"" space ":" space number
-            a-rest ::= additional-kvs
+            a-rest ::= ( "," space additional-kv )*
             additional-kv ::= string ":" space number
-            additional-kvs ::= additional-kv ( "," space additional-kv )*
             char ::= [^"\\] | "\\" (["\\/bfnrt] | "u" [0-9a-fA-F]{4})
             decimal-part ::= [0-9]{1,16}
             integral-part ::= [0] | [1-9] [0-9]{0,15}
             number ::= ("-"? integral-part) ("." decimal-part)? ([eE] [-+]? integral-part)? space
-            root ::= "{" space  (a-kv a-rest | additional-kvs )? "}" space
+            root ::= "{" space  (a-kv a-rest | additional-kv ( "," space additional-kv )* )? "}" space
             space ::= " "?
             string ::= "\"" char* "\"" space
         )"""
@@ -687,14 +684,13 @@ static void test_all(const std::string & lang, std::function<void(const TestCase
         R"""(
             a-kv ::= "\"a\"" space ":" space number
             additional-kv ::= string ":" space number
-            additional-kvs ::= additional-kv ( "," space additional-kv )*
             b-kv ::= "\"b\"" space ":" space number
-            b-rest ::= additional-kvs
+            b-rest ::= ( "," space additional-kv )*
             char ::= [^"\\] | "\\" (["\\/bfnrt] | "u" [0-9a-fA-F]{4})
             decimal-part ::= [0-9]{1,16}
             integral-part ::= [0] | [1-9] [0-9]{0,15}
             number ::= ("-"? integral-part) ("." decimal-part)? ([eE] [-+]? integral-part)? space
-            root ::= "{" space a-kv ( "," space ( b-kv b-rest | additional-kvs ) )? "}" space
+            root ::= "{" space a-kv ( "," space ( b-kv b-rest | additional-kv ( "," space additional-kv )* ) )? "}" space
             space ::= " "?
             string ::= "\"" char* "\"" space
         )"""
@@ -752,20 +748,18 @@ static void test_all(const std::string & lang, std::function<void(const TestCase
             alternative-0 ::= foo
             alternative-1 ::= bar
             array ::= "[" space ( value ("," space value)* )? "]" space
-            bar ::= "{" space  (bar-b-kv bar-b-rest | bar-additional-kvs )? "}" space
+            bar ::= "{" space  (bar-b-kv bar-b-rest | bar-additional-kv ( "," space bar-additional-kv )* )? "}" space
             bar-additional-kv ::= string ":" space bar-additional-value
-            bar-additional-kvs ::= bar-additional-kv ( "," space bar-additional-kv )*
             bar-additional-value ::= object
             bar-b-kv ::= "\"b\"" space ":" space number
-            bar-b-rest ::= bar-additional-kvs
+            bar-b-rest ::= ( "," space bar-additional-kv )*
             boolean ::= ("true" | "false") space
             char ::= [^"\\] | "\\" (["\\/bfnrt] | "u" [0-9a-fA-F]{4})
             decimal-part ::= [0-9]{1,16}
-            foo ::= "{" space  (foo-a-kv foo-a-rest | foo-additional-kvs )? "}" space
+            foo ::= "{" space  (foo-a-kv foo-a-rest | foo-additional-kv ( "," space foo-additional-kv )* )? "}" space
             foo-a-kv ::= "\"a\"" space ":" space number
-            foo-a-rest ::= foo-additional-kvs
+            foo-a-rest ::= ( "," space foo-additional-kv )*
             foo-additional-kv ::= string ":" space foo-additional-value
-            foo-additional-kvs ::= foo-additional-kv ( "," space foo-additional-kv )*
             foo-additional-value ::= object
             integral-part ::= [0] | [1-9] [0-9]{0,15}
             null ::= "null" space
@@ -775,7 +769,6 @@ static void test_all(const std::string & lang, std::function<void(const TestCase
             space ::= " "?
             string ::= "\"" char* "\"" space
             value ::= object | array | string | number | boolean | null
-
         )"""
     });