diff --git a/src/core/geometry/qgsrectangle.cpp b/src/core/geometry/qgsrectangle.cpp
index cdae2cb68dd..38084447034 100644
--- a/src/core/geometry/qgsrectangle.cpp
+++ b/src/core/geometry/qgsrectangle.cpp
@@ -254,7 +254,7 @@ QgsRectangle &QgsRectangle::operator+=( const QgsVector v )
 
 bool QgsRectangle::isEmpty() const
 {
-  return mXmax <= mXmin || mYmax <= mYmin;
+  return mXmax < mXmin || mYmax < mYmin || qgsDoubleNear( mXmax, mXmin ) || qgsDoubleNear( mYmax, mYmin );
 }
 
 bool QgsRectangle::isNull() const
diff --git a/tests/src/core/testqgsrectangle.cpp b/tests/src/core/testqgsrectangle.cpp
index bc1bd62a4f5..25350aea59f 100644
--- a/tests/src/core/testqgsrectangle.cpp
+++ b/tests/src/core/testqgsrectangle.cpp
@@ -25,13 +25,37 @@ class TestQgsRectangle: public QObject
 {
     Q_OBJECT
   private slots:
+    void isEmpty();
     void manipulate();
     void regression6194();
     void operators();
     void asVariant();
     void referenced();
+    void minimal();
+    void grow();
+    void include();
+    void buffered();
+    void isFinite();
+    void dataStream();
 };
 
+void TestQgsRectangle::isEmpty()
+{
+  QVERIFY( QgsRectangle().isEmpty() );
+  QVERIFY( QgsRectangle( 1, 2, 1, 4 ).isEmpty() );
+  QVERIFY( QgsRectangle( 2, 1, 4, 1 ).isEmpty() );
+  //constructor should normalize
+  QVERIFY( !QgsRectangle( 2, 2, 1, 4 ).isEmpty() );
+  QVERIFY( !QgsRectangle( 1, 2, 2, 1 ).isEmpty() );
+
+  QgsRectangle r( 2, 2, 3, 4 );
+  r.setXMaximum( 1 );
+  QVERIFY( r.isEmpty() );
+  r = QgsRectangle( 2, 2, 3, 4 );
+  r.setYMaximum( 1 );
+  QVERIFY( r.isEmpty() );
+}
+
 void TestQgsRectangle::manipulate()
 {
   // Set up two intersecting rectangles and normalize
@@ -155,5 +179,111 @@ void TestQgsRectangle::referenced()
   QCOMPARE( rect2.crs().authid(), QStringLiteral( "EPSG:28356" ) );
 }
 
+void TestQgsRectangle::minimal()
+{
+  QgsRectangle rect1 = QgsRectangle( 10.0, 20.0, 110.0, 220.0 );
+  rect1.setMinimal();
+  QVERIFY( rect1.isEmpty() );
+  QVERIFY( rect1.isNull() );
+}
+
+void TestQgsRectangle::grow()
+{
+  QgsRectangle rect1 = QgsRectangle( 10.0, 20.0, 110.0, 220.0 );
+  rect1.grow( 11 );
+  QCOMPARE( rect1.xMinimum(), -1.0 );
+  QCOMPARE( rect1.yMinimum(), 9.0 );
+  QCOMPARE( rect1.xMaximum(), 121.0 );
+  QCOMPARE( rect1.yMaximum(), 231.0 );
+
+  QgsRectangle rect2 = QgsRectangle( -110.0, -220.0, -10.0, -20.0 );
+  rect2.grow( 11 );
+  QCOMPARE( rect2.xMinimum(), -121.0 );
+  QCOMPARE( rect2.yMinimum(), -231.0 );
+  QCOMPARE( rect2.xMaximum(), 1.0 );
+  QCOMPARE( rect2.yMaximum(), -9.0 );
+}
+
+void TestQgsRectangle::include()
+{
+  QgsRectangle rect1 = QgsRectangle( 10.0, 20.0, 110.0, 220.0 );
+  // inside
+  rect1.include( QgsPointXY( 15, 50 ) );
+  QCOMPARE( rect1.xMinimum(), 10.0 );
+  QCOMPARE( rect1.yMinimum(), 20.0 );
+  QCOMPARE( rect1.xMaximum(), 110.0 );
+  QCOMPARE( rect1.yMaximum(), 220.0 );
+
+  rect1.include( QgsPointXY( 5, 50 ) );
+  QCOMPARE( rect1.xMinimum(), 5.0 );
+  QCOMPARE( rect1.yMinimum(), 20.0 );
+  QCOMPARE( rect1.xMaximum(), 110.0 );
+  QCOMPARE( rect1.yMaximum(), 220.0 );
+
+  rect1.include( QgsPointXY( 15, 12 ) );
+  QCOMPARE( rect1.xMinimum(), 5.0 );
+  QCOMPARE( rect1.yMinimum(), 12.0 );
+  QCOMPARE( rect1.xMaximum(), 110.0 );
+  QCOMPARE( rect1.yMaximum(), 220.0 );
+
+  rect1.include( QgsPointXY( 115, 12 ) );
+  QCOMPARE( rect1.xMinimum(), 5.0 );
+  QCOMPARE( rect1.yMinimum(), 12.0 );
+  QCOMPARE( rect1.xMaximum(), 115.0 );
+  QCOMPARE( rect1.yMaximum(), 220.0 );
+
+  rect1.include( QgsPointXY( 115, 242 ) );
+  QCOMPARE( rect1.xMinimum(), 5.0 );
+  QCOMPARE( rect1.yMinimum(), 12.0 );
+  QCOMPARE( rect1.xMaximum(), 115.0 );
+  QCOMPARE( rect1.yMaximum(), 242.0 );
+
+}
+
+void TestQgsRectangle::buffered()
+{
+  QgsRectangle rect = QgsRectangle( 10.0, 20.0, 110.0, 220.0 );
+  QgsRectangle rect1 = rect.buffered( 11 );
+  QCOMPARE( rect1.xMinimum(), -1.0 );
+  QCOMPARE( rect1.yMinimum(), 9.0 );
+  QCOMPARE( rect1.xMaximum(), 121.0 );
+  QCOMPARE( rect1.yMaximum(), 231.0 );
+
+  rect = QgsRectangle( -110.0, -220.0, -10.0, -20.0 );
+  QgsRectangle rect2 = rect.buffered( 11 );
+  QCOMPARE( rect2.xMinimum(), -121.0 );
+  QCOMPARE( rect2.yMinimum(), -231.0 );
+  QCOMPARE( rect2.xMaximum(), 1.0 );
+  QCOMPARE( rect2.yMaximum(), -9.0 );
+}
+
+void TestQgsRectangle::isFinite()
+{
+  QVERIFY( QgsRectangle( 1, 2, 3, 4 ).isFinite() );
+  QVERIFY( !QgsRectangle( std::numeric_limits<double>::infinity(), 2, 3, 4 ).isFinite() );
+  QVERIFY( !QgsRectangle( 1, std::numeric_limits<double>::infinity(), 3, 4 ).isFinite() );
+  QVERIFY( !QgsRectangle( 1, 2, std::numeric_limits<double>::infinity(), 4 ).isFinite() );
+  QVERIFY( !QgsRectangle( 1, 2, 3, std::numeric_limits<double>::infinity() ).isFinite() );
+  QVERIFY( !QgsRectangle( std::numeric_limits<double>::quiet_NaN(), 2, 3, 4 ).isFinite() );
+  QVERIFY( !QgsRectangle( 1, std::numeric_limits<double>::quiet_NaN(), 3, 4 ).isFinite() );
+  QVERIFY( !QgsRectangle( 1, 2, std::numeric_limits<double>::quiet_NaN(), 4 ).isFinite() );
+  QVERIFY( !QgsRectangle( 1, 2, 3, std::numeric_limits<double>::quiet_NaN() ).isFinite() );
+}
+
+void TestQgsRectangle::dataStream()
+{
+  QgsRectangle original( 10.1, 20.2, 110.3, 220.4 );
+
+  QByteArray ba;
+  QDataStream ds( &ba, QIODevice::ReadWrite );
+  ds << original;
+
+  QgsRectangle result;
+  ds.device()->seek( 0 );
+  ds >> result;
+
+  QCOMPARE( result, original );
+}
+
 QGSTEST_MAIN( TestQgsRectangle )
 #include "testqgsrectangle.moc"
diff --git a/tests/src/python/test_qgsrectangle.py b/tests/src/python/test_qgsrectangle.py
index 63c0f046103..195a7c0543f 100644
--- a/tests/src/python/test_qgsrectangle.py
+++ b/tests/src/python/test_qgsrectangle.py
@@ -24,17 +24,8 @@ start_app()
 
 class TestQgsRectangle(unittest.TestCase):
 
-    # Because isEmpty() is not returning expected result in 9b0fee3
-
-    @unittest.expectedFailure
     def testCtor(self):
         rect = QgsRectangle(5.0, 5.0, 10.0, 10.0)
-
-        myExpectedResult = True
-        myResult = rect.isEmpty()
-        myMessage = ('Expected: %s Got: %s' % (myExpectedResult, myResult))
-        assert rect.isEmpty(), myMessage
-
         myMessage = ('Expected: %s\nGot: %s\n' %
                      (5.0, rect.xMinimum()))
         assert rect.xMinimum() == 5.0, myMessage
@@ -204,6 +195,7 @@ class TestQgsRectangle(unittest.TestCase):
 
     def testToString(self):
         """Test the different string representations"""
+        self.assertEqual(QgsRectangle().toString(), 'Empty')
         rect = QgsRectangle(0, 0.1, 0.2, 0.3)
         myExpectedString = '0.0000000000000000,0.1000000000000000 : 0.2000000000000000,0.3000000000000000'
         myString = rect.toString()
@@ -211,6 +203,14 @@ class TestQgsRectangle(unittest.TestCase):
                      (myExpectedString, myString))
         assert myString == myExpectedString, myMessage
 
+        # can't test the actual result here, because floating point inaccuracies mean the result is unpredictable
+        # at this precision
+        self.assertEqual(len(rect.toString(20)), 93)
+
+        myMessage = ('Expected: %s\nGot: %s\n' %
+                     (myExpectedString, myString))
+        assert myString == myExpectedString, myMessage
+
         myExpectedString = '0,0 : 0,0'
         myString = rect.toString(0)
         myMessage = ('Expected: %s\nGot: %s\n' %
@@ -242,6 +242,11 @@ class TestQgsRectangle(unittest.TestCase):
                      (myExpectedString, myString))
         assert myString == myExpectedString, myMessage
 
+    def testAsPolygon(self):
+        """Test string representation as polygon"""
+        self.assertEqual(QgsRectangle().asPolygon(), '0.00000000 0.00000000, 0.00000000 0.00000000, 0.00000000 0.00000000, 0.00000000 0.00000000, 0.00000000 0.00000000')
+        self.assertEqual(QgsRectangle(0, 0.1, 0.2, 0.3).asPolygon(), '0.00000000 0.10000000, 0.00000000 0.30000000, 0.20000000 0.30000000, 0.20000000 0.10000000, 0.00000000 0.10000000')
+
     def testToBox3d(self):
         rect = QgsRectangle(0, 0.1, 0.2, 0.3)
         box = rect.toBox3d(0.4, 0.5)
@@ -261,6 +266,14 @@ class TestQgsRectangle(unittest.TestCase):
         rect1 -= rect1.center() - QgsPointXY(0, 0)
         assert rect1.center() == QgsPointXY(0, 0)
 
+    def testInvert(self):
+        rect = QgsRectangle(0, 0.1, 0.2, 0.3)
+        rect.invert()
+        self.assertEqual(rect.xMinimum(), 0.1)
+        self.assertEqual(rect.yMinimum(), 0)
+        self.assertEqual(rect.xMaximum(), 0.3)
+        self.assertEqual(rect.yMaximum(), 0.2)
+
 
 if __name__ == '__main__':
     unittest.main()