DataGridView: Copy complete to clipboard

I have a DataGridView in a .Net application (V4 C# VS2010) & want to copy all the data to the clipboard on the click of a button. No problem -

private void copyToClipboard()
{
    dataGridView1.SelectAll();
    DataObject dataObj = dataGridView1.GetClipboardContent();
    if (dataObj != null)
        Clipboard.SetDataObject(dataObj);
}

Problem is that the user might already have some cells, rows etc selected on the DataGrid & I don't really want to change that selection. The above obviously selects everything. I could dataGridView1.ClearSelection(); at the end which is marginally better but still doesn't achieve what's required.

I can save the selected cells:

var mySelectedCells = dataGridView1.SelectedCells;

but how do I get those selected cells reselected on the DataGrid after the copy? Is there an easy way to get the selected cells collection back into the DataGrid? Perhaps there is a better way to get the whole grid copied to the clipboard in the first place without affecting presently selected cells?