Changing Floating DocumentWindow Style

I've figured out how to change the DocumentWindow tab colors via a Style. The issue now is that I'm not having any luck changing the look of the window when it's rafted. I'd like to change both the header and the border. Is this something that I can do easily via a Style or will I have to change the ControlTemplate? The Style I'm using looks like

    <Style x:Key="{x:Type docking:DocumentWindow}" TargetType="{x:Type docking:DocumentWindow}">
      <Setter Property="TabBackground" Value="LightGray" />
      <Setter Property="TabBorderBrush" Value="DimGray" />
      <Setter Property="TabForeground" Value="Black" />
      <Style.Triggers>
        <Trigger Property="IsMouseOver" Value="True">
          <Setter Property="TabBackground" Value="AliceBlue" />
          <Setter Property="TabBorderBrush" Value="LightBlue" />
          <Setter Property="TabForeground" Value="Black" />
        </Trigger>
        <Trigger Property="IsSelected" Value="True">
          <Setter Property="TabBackground" Value="AliceBlue" />
          <Setter Property="TabBorderBrush" Value="DimGray" />
          <Setter Property="TabForeground" Value="Black" />
        </Trigger>
      </Style.Triggers>
    </Style>

And for right now I'd like to have the border and background of the title bar be LightBlue.