diff --git a/samples/grid/griddemo.cpp b/samples/grid/griddemo.cpp
index b02ef8c0f9..013afb6045 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");
 
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 7277ab8817..23de3046a5 100644
--- a/tests/controls/gridtest.cpp
+++ b/tests/controls/gridtest.cpp
@@ -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]")