diff --git a/include/wx/generic/grid.h b/include/wx/generic/grid.h
index b01c6b4e54..a06c654855 100644
--- a/include/wx/generic/grid.h
+++ b/include/wx/generic/grid.h
@@ -2218,10 +2218,14 @@ private:
     // SetColPos() and ResetColPos())
     void RefreshAfterColPosChange();
 
-    // reset the variables used during dragging operations after it ended
-    // because we lost mouse capture
+    // reset the variables used during dragging operations after it ended,
+    // either because we called EndDraggingIfNecessary() ourselves or because
+    // we lost mouse capture
     void DoAfterDraggingEnd();
 
+    // release the mouse capture if it's currently captured
+    void EndDraggingIfNecessary();
+
 
     // return the position (not index) of the column at the given logical pixel
     // position
@@ -2242,8 +2246,12 @@ private:
     // process row/column resizing drag event
     void DoGridLineDrag(wxMouseEvent& event, const wxGridOperations& oper);
 
-    // process mouse drag event in the grid window
-    void DoGridDragEvent(wxMouseEvent& event, const wxGridCellCoords& coords);
+    // process mouse drag event in the grid window, return false if starting
+    // dragging was vetoed by the user-defined wxEVT_GRID_CELL_BEGIN_DRAG
+    // handler
+    bool DoGridDragEvent(wxMouseEvent& event,
+                         const wxGridCellCoords& coords,
+                         bool isFirstDrag);
 
     // process different clicks on grid cells
     void DoGridCellLeftDown(wxMouseEvent& event,
diff --git a/src/generic/grid.cpp b/src/generic/grid.cpp
index c3ab7f0594..2f01b2f667 100644
--- a/src/generic/grid.cpp
+++ b/src/generic/grid.cpp
@@ -3863,6 +3863,16 @@ void wxGrid::DoAfterDraggingEnd()
     m_winCapture = NULL;
 }
 
+void wxGrid::EndDraggingIfNecessary()
+{
+    if ( m_winCapture )
+    {
+        m_winCapture->ReleaseMouse();
+
+        DoAfterDraggingEnd();
+    }
+}
+
 void wxGrid::ChangeCursorMode(CursorMode mode,
                               wxWindow *win,
                               bool captureMouse)
@@ -3897,11 +3907,7 @@ void wxGrid::ChangeCursorMode(CursorMode mode,
         win = m_gridWin;
     }
 
-    if ( m_winCapture )
-    {
-        m_winCapture->ReleaseMouse();
-        m_winCapture = NULL;
-    }
+    EndDraggingIfNecessary();
 
     m_cursorMode = mode;
 
@@ -4019,34 +4025,14 @@ void wxGrid::DoGridLineDrag(wxMouseEvent& event, const wxGridOperations& oper)
     oper.DrawParallelLineInRect(dc, rectWin, m_dragLastPos);
 }
 
-void wxGrid::DoGridDragEvent(wxMouseEvent& event, const wxGridCellCoords& coords)
+bool wxGrid::DoGridDragEvent(wxMouseEvent& event,
+                             const wxGridCellCoords& coords,
+                             bool isFirstDrag)
 {
-    if ( !m_isDragging )
-    {
-        // Don't start doing anything until the mouse has been dragged far
-        // enough
-        const wxPoint& pt = event.GetPosition();
-        if ( m_startDragPos == wxDefaultPosition )
-        {
-            m_startDragPos = pt;
-            return;
-        }
-
-        if ( abs(m_startDragPos.x - pt.x) <= DRAG_SENSITIVITY &&
-                abs(m_startDragPos.y - pt.y) <= DRAG_SENSITIVITY )
-            return;
-    }
-
-    const bool isFirstDrag = !m_isDragging;
-    m_isDragging = true;
-
     switch ( m_cursorMode )
     {
         case WXGRID_CURSOR_SELECT_CELL:
-            // no further handling if handled by user
-            if ( DoGridCellDrag(event, coords, isFirstDrag) == false )
-                return;
-            break;
+            return DoGridCellDrag(event, coords, isFirstDrag);
 
         case WXGRID_CURSOR_RESIZE_ROW:
             DoGridLineDrag(event, wxGridRowOperations());
@@ -4060,13 +4046,7 @@ void wxGrid::DoGridDragEvent(wxMouseEvent& event, const wxGridCellCoords& coords
             event.Skip();
     }
 
-    if ( isFirstDrag )
-    {
-        wxASSERT_MSG( !m_winCapture, "shouldn't capture the mouse twice" );
-
-        m_winCapture = m_gridWin;
-        m_winCapture->CaptureMouse();
-    }
+    return true;
 }
 
 void
@@ -4160,12 +4140,6 @@ wxGrid::DoGridCellLeftUp(wxMouseEvent& event, const wxGridCellCoords& coords)
 {
     if ( m_cursorMode == WXGRID_CURSOR_SELECT_CELL )
     {
-        if (m_winCapture)
-        {
-            m_winCapture->ReleaseMouse();
-            m_winCapture = NULL;
-        }
-
         if ( coords == m_currentCellCoords && m_waitForSlowClick && CanEnableCellControl() )
         {
             ClearSelection();
@@ -4266,14 +4240,6 @@ wxGrid::DoGridMouseMoveEvent(wxMouseEvent& WXUNUSED(event),
 
 void wxGrid::ProcessGridCellMouseEvent(wxMouseEvent& event)
 {
-    if ( event.Entering() || event.Leaving() )
-    {
-        // we don't care about these events but we must not reset m_isDragging
-        // if they happen so return before anything else is done
-        event.Skip();
-        return;
-    }
-
     const wxPoint pos = CalcUnscrolledPosition(event.GetPosition());
 
     // coordinates of the cell under mouse
@@ -4287,17 +4253,64 @@ void wxGrid::ProcessGridCellMouseEvent(wxMouseEvent& event)
         coords.SetCol(coords.GetCol() + cell_cols);
     }
 
-    if ( event.Dragging() )
+    // Releasing the left mouse button must be processed in any case, so deal
+    // with it first.
+    if ( event.LeftUp() )
     {
-        if ( event.LeftIsDown() )
-            DoGridDragEvent(event, coords);
-        else
-            event.Skip();
+        // Note that we must call this one first, before resetting the
+        // drag-related data, as it relies on m_cursorMode being still set and
+        // EndDraggingIfNecessary() resets it.
+        DoGridCellLeftUp(event, coords);
+
+        EndDraggingIfNecessary();
         return;
     }
 
-    m_isDragging = false;
-    m_startDragPos = wxDefaultPosition;
+    const bool isDraggingWithLeft = event.Dragging() && event.LeftIsDown();
+
+    // While dragging the mouse, only releasing the left mouse button, which
+    // cancels the drag operation, is processed (above) and any other events
+    // are just ignored while it's in progress.
+    if ( m_isDragging )
+    {
+        if ( isDraggingWithLeft )
+            DoGridDragEvent(event, coords, false /* not first drag */);
+        return;
+    }
+
+    // Now check if we're starting a drag operation (if it had been already
+    // started, m_isDragging would be true above).
+    if ( isDraggingWithLeft )
+    {
+        // To avoid accidental drags, don't start doing anything until the
+        // mouse has been dragged far enough.
+        const wxPoint& pt = event.GetPosition();
+        if ( m_startDragPos == wxDefaultPosition )
+        {
+            m_startDragPos = pt;
+            return;
+        }
+
+        if ( abs(m_startDragPos.x - pt.x) <= DRAG_SENSITIVITY &&
+                abs(m_startDragPos.y - pt.y) <= DRAG_SENSITIVITY )
+            return;
+
+        if ( DoGridDragEvent(event, coords, true /* first drag */) )
+        {
+            wxASSERT_MSG( !m_winCapture, "shouldn't capture the mouse twice" );
+
+            m_winCapture = m_gridWin;
+            m_winCapture->CaptureMouse();
+
+            m_isDragging = true;
+        }
+
+        return;
+    }
+
+    // If we're not dragging, cancel any dragging operation which could have
+    // been in progress.
+    EndDraggingIfNecessary();
 
     // deal with various button presses
     if ( event.IsButton() )
@@ -4315,12 +4328,6 @@ void wxGrid::ProcessGridCellMouseEvent(wxMouseEvent& event)
             else if ( event.RightDClick() )
                 SendEvent(wxEVT_GRID_CELL_RIGHT_DCLICK, coords, event);
         }
-
-        // this one should be called even if we're not over any cell
-        if ( event.LeftUp() )
-        {
-            DoGridCellLeftUp(event, coords);
-        }
     }
     else if ( event.Moving() )
     {