Advmemo Scrollbar

AdvMemo's vertical scrollbar does not seem to position properly after text is programatically added to the memo. Drop an advmemo on a form and a button with the following handler:

procedure TForm9.Button1Click(Sender: TObject);
var
  I: Integer;
begin
  for I := 1 to 30 do
  begin
    AdvMemo1.lines.add(IntToStr(I));
    Memo1.Lines.Add(inttostr(I));
  end;
  AdvMemo1.ScrollToBottom;
end;

Run the program and click the button. Result: the vertical scrollbar is in roughly the center of the memo, not at the bottom. I suspect this relates to the presence of "dead space" in the control following the last line of the memo. Is there a way to get rid of that space and have the vertical scrollbar position itself at the bottom of the scrollbar? 

This is by design as the TAdvMemo allows to scroll till the last line is at the top, so, even at the end, new text can be added on a full page.