diff --git a/src/corelib/serialization/qcbormap.cpp b/src/corelib/serialization/qcbormap.cpp
index 9367a2ab9b2..00c0bb0b6d2 100644
--- a/src/corelib/serialization/qcbormap.cpp
+++ b/src/corelib/serialization/qcbormap.cpp
@@ -19,7 +19,7 @@ using namespace QtCbor;
     \brief The QCborMap class is used to hold an associative container representable in CBOR.
 
     \compares strong
-    \compareswith strong QCborValue
+    \compareswith strong QCborValue QCborValueConstRef
     \endcompareswith
 
     This class can be used to hold an associative container in CBOR, a map
diff --git a/src/corelib/serialization/qcbormap.h b/src/corelib/serialization/qcbormap.h
index 55935e113ec..087334fdffe 100644
--- a/src/corelib/serialization/qcbormap.h
+++ b/src/corelib/serialization/qcbormap.h
@@ -326,6 +326,19 @@ private:
     }
     Q_DECLARE_STRONGLY_ORDERED(QCborMap, QCborValue)
 
+    friend bool comparesEqual(const QCborMap &lhs, const QCborValueConstRef &rhs) noexcept
+    {
+        return lhs.compare(rhs.toMap()) == 0;
+    }
+
+    friend Qt::strong_ordering compareThreeWay(const QCborMap &lhs,
+                                               const QCborValueConstRef &rhs) noexcept
+    {
+        int c = lhs.compare(rhs.toMap());
+        return Qt::compareThreeWay(c, 0);
+    }
+    Q_DECLARE_STRONGLY_ORDERED(QCborMap, QCborValueConstRef)
+
     explicit QCborMap(QCborContainerPrivate &dd) noexcept;
     QExplicitlySharedDataPointer<QCborContainerPrivate> d;
 };
diff --git a/tests/auto/corelib/serialization/qcborvalue/tst_qcborvalue.cpp b/tests/auto/corelib/serialization/qcborvalue/tst_qcborvalue.cpp
index e3544a4056e..37f1569bbc8 100644
--- a/tests/auto/corelib/serialization/qcborvalue/tst_qcborvalue.cpp
+++ b/tests/auto/corelib/serialization/qcborvalue/tst_qcborvalue.cpp
@@ -452,17 +452,25 @@ void tst_QCborValue::extendedTypes_data()
 
 void tst_QCborValue::compareCompiles()
 {
+    // homogeneous types
     QTestPrivate::testAllComparisonOperatorsCompile<QCborValue>();
     QTestPrivate::testAllComparisonOperatorsCompile<QCborValueRef>();
     QTestPrivate::testAllComparisonOperatorsCompile<QCborValueConstRef>();
     QTestPrivate::testAllComparisonOperatorsCompile<QCborArray>();
     QTestPrivate::testAllComparisonOperatorsCompile<QCborMap>();
+
+    // QCborValue, Ref and ConstRef
     QTestPrivate::testAllComparisonOperatorsCompile<QCborValueRef, QCborValueConstRef>();
     QTestPrivate::testAllComparisonOperatorsCompile<QCborValueConstRef, QCborValue>();
     QTestPrivate::testAllComparisonOperatorsCompile<QCborValueRef, QCborValue>();
-    QTestPrivate::testAllComparisonOperatorsCompile<QCborValueConstRef, QCborArray>();
-    QTestPrivate::testAllComparisonOperatorsCompile<QCborValueRef, QCborArray>();
+
+    // QCbor{Array,Map} <=> QCborValue{,Ref,ConstRef}
+    QTestPrivate::testAllComparisonOperatorsCompile<QCborArray, QCborValue>();
+    QTestPrivate::testAllComparisonOperatorsCompile<QCborArray, QCborValueRef>();
+    QTestPrivate::testAllComparisonOperatorsCompile<QCborArray, QCborValueConstRef>();
     QTestPrivate::testAllComparisonOperatorsCompile<QCborMap, QCborValue>();
+    QTestPrivate::testAllComparisonOperatorsCompile<QCborMap, QCborValueRef>();
+    QTestPrivate::testAllComparisonOperatorsCompile<QCborMap, QCborValueConstRef>();
 }
 
 void tst_QCborValue::extendedTypes()