diff --git a/samples/grid/griddemo.cpp b/samples/grid/griddemo.cpp
index b02ef8c0f9..62560cc04a 100644
--- a/samples/grid/griddemo.cpp
+++ b/samples/grid/griddemo.cpp
@@ -614,6 +614,7 @@ GridFrame::GridFrame()
     grid->SetRowSize(10, 30);
     attr = new wxGridCellAttr;
     attr->SetBackgroundColour(*wxLIGHT_GREY);
+    attr->SetAlignment(wxALIGN_INVALID, wxALIGN_CENTRE);
     grid->SetRowAttr(10, attr);
     grid->SetCellValue(10, 0, "You can't resize this row interactively -- try it");
 
@@ -1604,8 +1605,7 @@ MyGridCellAttrProvider::MyGridCellAttrProvider()
 wxGridCellAttr *MyGridCellAttrProvider::GetAttr(int row, int col,
                            wxGridCellAttr::wxAttrKind  kind /* = wxGridCellAttr::Any */) const
 {
-    wxObjectDataPtr<wxGridCellAttr>
-        attr(wxGridCellAttrProvider::GetAttr(row, col, kind));
+    wxGridCellAttrPtr attr(wxGridCellAttrProvider::GetAttr(row, col, kind));
 
     if ( row % 2 )
     {
diff --git a/samples/grid/griddemo.h b/samples/grid/griddemo.h
index 68319b204a..784e0fca3d 100644
--- a/samples/grid/griddemo.h
+++ b/samples/grid/griddemo.h
@@ -301,7 +301,7 @@ public:
                                     wxGridCellAttr::wxAttrKind  kind) const wxOVERRIDE;
 
 private:
-    wxObjectDataPtr<wxGridCellAttr> m_attrForOddRows;
+    wxGridCellAttrPtr m_attrForOddRows;
 };
 
 // ----------------------------------------------------------------------------
diff --git a/src/generic/grid.cpp b/src/generic/grid.cpp
index ad0f62d585..f4196a3969 100644
--- a/src/generic/grid.cpp
+++ b/src/generic/grid.cpp
@@ -647,9 +647,17 @@ wxGridFitMode wxGridCellAttr::GetFitMode() const
 
 bool wxGridCellAttr::CanOverflow() const
 {
-    int hAlign;
-    GetAlignment(&hAlign, NULL);
-    return GetOverflow() && (hAlign == wxALIGN_LEFT);
+    // If overflow is disabled anyhow, we definitely can't overflow.
+    if ( !GetOverflow() )
+        return false;
+
+    // But if it is enabled, we still don't use it for right-aligned or
+    // centered cells because it's not really clear how it should work for
+    // them.
+    int hAlign = wxALIGN_LEFT;
+    GetNonDefaultAlignment(&hAlign, NULL);
+
+    return hAlign == wxALIGN_LEFT;
 }
 
 // GetRenderer and GetEditor use a slightly different decision path about
diff --git a/tests/controls/gridtest.cpp b/tests/controls/gridtest.cpp
index 735d571d70..23de3046a5 100644
--- a/tests/controls/gridtest.cpp
+++ b/tests/controls/gridtest.cpp
@@ -899,7 +899,7 @@ TEST_CASE_METHOD(GridTestCase, "Grid::GetNonDefaultAlignment", "[grid]")
     // GetNonDefaultAlignment() is used by several renderers having their own
     // preferred alignment, so check that if we don't reset the alignment
     // explicitly, it doesn't override the alignment used by default.
-    wxGridCellAttr* attr = NULL;
+    wxGridCellAttrPtr attr;
     int hAlign = wxALIGN_RIGHT,
         vAlign = wxALIGN_INVALID;
 
@@ -925,6 +925,14 @@ TEST_CASE_METHOD(GridTestCase, "Grid::GetNonDefaultAlignment", "[grid]")
     attr->GetNonDefaultAlignment(&hAlign, &vAlign);
     CHECK( hAlign == wxALIGN_RIGHT );
     CHECK( vAlign == wxALIGN_CENTRE_VERTICAL );
+
+    // This is only indirectly related, but test here for CanOverflow() working
+    // correctly for the cells with non-default alignment, as this used to be
+    // broken.
+    m_grid->SetCellAlignment(0, 0, wxALIGN_INVALID, wxALIGN_CENTRE);
+    attr = m_grid->CallGetCellAttr(0, 0);
+    REQUIRE( attr );
+    CHECK( attr->CanOverflow() );
 }
 
 TEST_CASE_METHOD(GridTestCase, "Grid::Editable", "[grid]")
@@ -1174,9 +1182,9 @@ TEST_CASE_METHOD(GridTestCase, "Grid::AutoSizeColumn", "[grid]")
     // Hardcoded extra margin for the columns used in grid.cpp.
     const int margin = m_grid->FromDIP(10);
 
-    wxGridCellAttr *attr = m_grid->GetOrCreateCellAttr(0, 0);
-    wxGridCellRenderer *renderer = attr->GetRenderer(m_grid, 0, 0);
-    REQUIRE(renderer != NULL);
+    wxGridCellAttrPtr attr(m_grid->GetOrCreateCellAttr(0, 0));
+    wxGridCellRendererPtr renderer(attr->GetRenderer(m_grid, 0, 0));
+    REQUIRE(renderer);
 
     wxClientDC dcCell(m_grid->GetGridWindow());