diff --git a/include/xgboost/json.h b/include/xgboost/json.h
index 97dc2e11d..cdd86d135 100644
--- a/include/xgboost/json.h
+++ b/include/xgboost/json.h
@@ -202,6 +202,17 @@ class JsonInteger : public Value {
             typename std::enable_if<std::is_same<IntT, size_t>::value>::type* = nullptr>
   JsonInteger(IntT value) : Value(ValueKind::Integer),  // NOLINT
                             integer_{static_cast<Int>(value)} {}
+  template <typename IntT,
+            typename std::enable_if<std::is_same<IntT, int32_t>::value>::type* = nullptr>
+  JsonInteger(IntT value) : Value(ValueKind::Integer),  // NOLINT
+                            integer_{static_cast<Int>(value)} {}
+  template <typename IntT,
+            typename std::enable_if<
+                std::is_same<IntT, uint32_t>::value &&
+                !std::is_same<std::size_t, uint32_t>::value>::type * = nullptr>
+  JsonInteger(IntT value)  // NOLINT
+      : Value(ValueKind::Integer),
+        integer_{static_cast<Int>(value)} {}
 
   Json& operator[](std::string const & key) override;
   Json& operator[](int ind) override;
@@ -533,8 +544,8 @@ using Null    = JsonNull;
 
 // Utils tailored for XGBoost.
 
-template <typename Type>
-Object toJson(XGBoostParameter<Type> const& param) {
+template <typename Parameter>
+Object toJson(Parameter const& param) {
   Object obj;
   for (auto const& kv : param.__DICT__()) {
     obj[kv.first] = kv.second;
@@ -542,8 +553,8 @@ Object toJson(XGBoostParameter<Type> const& param) {
   return obj;
 }
 
-template <typename Type>
-void fromJson(Json const& obj, XGBoostParameter<Type>* param) {
+template <typename Parameter>
+void fromJson(Json const& obj, Parameter* param) {
   auto const& j_param = get<Object const>(obj);
   std::map<std::string, std::string> m;
   for (auto const& kv : j_param) {
diff --git a/src/common/json.cc b/src/common/json.cc
index 2c8000787..915619924 100644
--- a/src/common/json.cc
+++ b/src/common/json.cc
@@ -243,7 +243,7 @@ Json& JsonNumber::operator[](int ind) {
 
 bool JsonNumber::operator==(Value const& rhs) const {
   if (!IsA<JsonNumber>(&rhs)) { return false; }
-  return number_ == Cast<JsonNumber const>(&rhs)->getNumber();
+  return std::abs(number_ - Cast<JsonNumber const>(&rhs)->getNumber()) < kRtEps;
 }
 
 Value & JsonNumber::operator=(Value const &rhs) {
@@ -504,7 +504,10 @@ Json JsonReader::ParseObject() {
   SkipSpaces();
   char ch = PeekNextChar();
 
-  if (ch == '}') return Json(std::move(data));
+  if (ch == '}') {
+    GetChar('}');
+    return Json(std::move(data));
+  }
 
   while (true) {
     SkipSpaces();
diff --git a/tests/cpp/common/test_json.cc b/tests/cpp/common/test_json.cc
index 94e87bcac..c4adbb42e 100644
--- a/tests/cpp/common/test_json.cc
+++ b/tests/cpp/common/test_json.cc
@@ -226,6 +226,10 @@ TEST(Json, EmptyObject) {
   std::stringstream iss(str);
   auto json = Json::Load(StringView{str.c_str(), str.size()});
   ASSERT_TRUE(IsA<Object>(json["statistic"]));
+
+  str = R"json({"Config": {},"Model": {}})json"; // NOLINT
+  json = Json::Load(StringView{str.c_str(), str.size()});
+  ASSERT_TRUE(IsA<Object>(json["Model"]));
 }
 
 TEST(Json, EmptyArray) {