diff --git a/src/core/geometry/qgscompoundcurve.cpp b/src/core/geometry/qgscompoundcurve.cpp
index 724c610cd09..af793f5af26 100644
--- a/src/core/geometry/qgscompoundcurve.cpp
+++ b/src/core/geometry/qgscompoundcurve.cpp
@@ -825,6 +825,7 @@ bool QgsCompoundCurve::deleteVertex( QgsVertexId position )
       removeCurve( curveId );
     }
   }
+  // We are on a vertex that belongs to two curves
   else if ( curveIds.size() == 2 )
   {
     const int nextCurveId = curveIds.at( 1 ).first;
@@ -835,46 +836,51 @@ bool QgsCompoundCurve::deleteVertex( QgsVertexId position )
     Q_ASSERT( subVertexId.vertex == curve->numPoints() - 1 );
     Q_ASSERT( nextSubVertexId.vertex == 0 );
 
+    // globals start and end points
     const QgsPoint startPoint = curve->startPoint();
     const QgsPoint endPoint = nextCurve->endPoint();
 
-    if ( QgsWkbTypes::flatType( curve->wkbType() ) == Qgis::WkbType::LineString &&
-         QgsWkbTypes::flatType( nextCurve->wkbType() ) == Qgis::WkbType::CircularString &&
-         nextCurve->numPoints() > 3 )
-    {
-      QgsPoint intermediatePoint;
-      Qgis::VertexType type;
-      nextCurve->pointAt( 2, intermediatePoint, type );
-      curve->moveVertex( QgsVertexId( 0, 0, curve->numPoints() - 1 ), intermediatePoint );
-    }
-    else if ( !curve->deleteVertex( subVertexId ) )
+    // delete the vertex on first curve
+    if ( !curve->deleteVertex( subVertexId ) )
     {
       clearCache(); //bbox may have changed
       return false;
     }
-    if ( QgsWkbTypes::flatType( curve->wkbType() ) == Qgis::WkbType::CircularString &&
-         curve->numPoints() > 0 &&
-         QgsWkbTypes::flatType( nextCurve->wkbType() ) == Qgis::WkbType::LineString )
-    {
-      QgsPoint intermediatePoint = curve->endPoint();
-      nextCurve->moveVertex( QgsVertexId( 0, 0, 0 ), intermediatePoint );
-    }
-    else if ( !nextCurve->deleteVertex( nextSubVertexId ) )
+
+    // delete the vertex on second curve
+    if ( !nextCurve->deleteVertex( nextSubVertexId ) )
     {
       clearCache(); //bbox may have changed
       return false;
     }
-    if ( curve->numPoints() == 0 &&
-         nextCurve->numPoints() != 0 )
+
+    // if first curve is now empty and second is not then
+    // create a LineString to link from the global start point to the
+    // new start of the second curve and delete the first curve
+    if ( curve->numPoints() == 0 && nextCurve->numPoints() != 0 )
     {
-      nextCurve->moveVertex( QgsVertexId( 0, 0, 0 ), startPoint );
+      QgsPoint startPointOfSecond = nextCurve->startPoint();
       removeCurve( curveId );
+      QgsLineString *line = new QgsLineString();
+      line->insertVertex( QgsVertexId( 0, 0, 0 ), startPoint );
+      line->insertVertex( QgsVertexId( 0, 0, 1 ), startPointOfSecond );
+      mCurves.insert( curveId, line );
     }
+    // else, if the first curve is not empty and the second is
+    // then create a LineString to link from the new end of the first curve to the
+    // global end point and delete the first curve
     else if ( curve->numPoints() != 0 && nextCurve->numPoints() == 0 )
     {
-      curve->moveVertex( QgsVertexId( 0, 0, curve->numPoints() - 1 ), endPoint );
+      QgsPoint endPointOfFirst = curve->endPoint();
       removeCurve( nextCurveId );
+      QgsLineString *line = new QgsLineString();
+      line->insertVertex( QgsVertexId( 0, 0, 0 ), endPointOfFirst );
+      line->insertVertex( QgsVertexId( 0, 0, 1 ), endPoint );
+      mCurves.insert( nextCurveId, line );
     }
+    // else, if both curves are empty then
+    // remove both curves and create a LineString to link
+    // the curves before and the curves after the whole geometry
     else if ( curve->numPoints() == 0 &&
               nextCurve->numPoints() == 0 )
     {
@@ -885,6 +891,8 @@ bool QgsCompoundCurve::deleteVertex( QgsVertexId position )
       line->insertVertex( QgsVertexId( 0, 0, 1 ), endPoint );
       mCurves.insert( curveId, line );
     }
+    // else, both curves still have vertices, create a LineString to link
+    // the curves if needed
     else
     {
       QgsPoint endPointOfFirst = curve->endPoint();
@@ -897,6 +905,7 @@ bool QgsCompoundCurve::deleteVertex( QgsVertexId position )
         mCurves.insert( nextCurveId, line );
       }
     }
+    condenseCurves(); // We merge consecutive LineStrings and CircularStrings
   }
 
   bool success = !curveIds.isEmpty();
diff --git a/tests/src/core/geometry/testqgscompoundcurve.cpp b/tests/src/core/geometry/testqgscompoundcurve.cpp
index 9659863c2ea..25f44dcb69d 100644
--- a/tests/src/core/geometry/testqgscompoundcurve.cpp
+++ b/tests/src/core/geometry/testqgscompoundcurve.cpp
@@ -1488,7 +1488,7 @@ void TestQgsCompoundCurve::deleteVertex()
   cc.deleteVertex( QgsVertexId( 0, 0, 2 ) );
   QCOMPARE( cc.numPoints(), 0 );
 
-  // two lines
+  // two lines, small line first and long line second
   QgsLineString ls;
   ls.setPoints( QgsPointSequence() << QgsPoint( Qgis::WkbType::PointZM, 1, 2, 2, 3 )
                 << QgsPoint( Qgis::WkbType::PointZM, 11, 12, 4, 5 ) );
@@ -1506,19 +1506,20 @@ void TestQgsCompoundCurve::deleteVertex()
 
   const QgsLineString *lsPtr = dynamic_cast< const QgsLineString * >( cc.curveAt( 0 ) );
 
-  QCOMPARE( lsPtr->numPoints(), 2 );
+  QCOMPARE( lsPtr->numPoints(), 3 );
   QCOMPARE( lsPtr->startPoint(), QgsPoint( Qgis::WkbType::PointZM, 1, 2, 2, 3 ) );
   QCOMPARE( lsPtr->endPoint(), QgsPoint( Qgis::WkbType::PointZM, 31, 42, 4, 5 ) );
 
   //add vertex at the end of linestring
-  QVERIFY( cc.insertVertex( QgsVertexId( 0, 0, 2 ), QgsPoint( Qgis::WkbType::PointZM, 35, 43, 4, 5 ) ) );
+  QVERIFY( cc.insertVertex( QgsVertexId( 0, 0, 3 ), QgsPoint( Qgis::WkbType::PointZM, 35, 43, 4, 5 ) ) );
 
   lsPtr = dynamic_cast< const QgsLineString * >( cc.curveAt( 0 ) );
 
-  QCOMPARE( lsPtr->numPoints(), 3 );
+  QCOMPARE( lsPtr->numPoints(), 4 );
   QCOMPARE( lsPtr->startPoint(), QgsPoint( Qgis::WkbType::PointZM, 1, 2, 2, 3 ) );
   QCOMPARE( lsPtr->endPoint(), QgsPoint( Qgis::WkbType::PointZM, 35, 43, 4, 5 ) );
 
+  // two lines, long line first and small line second
   ls.setPoints( QgsPointSequence() << QgsPoint( Qgis::WkbType::PointZM, 1, 2, 2, 3 )
                 << QgsPoint( Qgis::WkbType::PointZM, 11, 12, 4, 5 )
                 << QgsPoint( Qgis::WkbType::PointZM, 21, 32, 4, 5 ) );
@@ -1535,9 +1536,22 @@ void TestQgsCompoundCurve::deleteVertex()
 
   lsPtr = dynamic_cast< const QgsLineString * >( cc.curveAt( 0 ) );
 
-  QCOMPARE( lsPtr->numPoints(), 2 );
+  QCOMPARE( lsPtr->numPoints(), 3 );
   QCOMPARE( lsPtr->startPoint(), QgsPoint( Qgis::WkbType::PointZM, 1, 2, 2, 3 ) );
   QCOMPARE( lsPtr->endPoint(), QgsPoint( Qgis::WkbType::PointZM, 31, 42, 4, 5 ) );
+
+  // small ("one-curve" i.e. 3 vertices total) CircularString followed by LineString
+  cc.clear();
+  cs.setPoints( QgsPointSequence() << QgsPoint( 0, 0 ) << QgsPoint( 1, 1 ) << QgsPoint( 0, 2 ) );
+  ls.setPoints( QgsPointSequence() << QgsPoint( 0, 2 ) << QgsPoint( 0, 3 ) << QgsPoint( 0, 4 ) );
+  cc.addCurve( cs.clone() );
+  cc.addCurve( ls.clone() );
+
+  QCOMPARE( cc.nCurves(), 2 );
+  QCOMPARE( cc.numPoints(), 5 );
+  QVERIFY( cc.deleteVertex( QgsVertexId( 0, 0, 2 ) ) );
+  QCOMPARE( cc.nCurves(), 1 );
+  QCOMPARE( cc.numPoints(), 3 );
 }
 
 void TestQgsCompoundCurve::filterVertices()