Vista - Tooltip ControlTemplate

I decided to do some artistic thingy to my tooltips:

<Style TargetType="{x:Type ToolTip}">
<Setter Property="ToolTip.Background">
<Setter.Value>
<RadialGradientBrush Center="0,0" RadiusX="0.9" RadiusY="0.9"
GradientOrigin="0,0" >
<RadialGradientBrush.GradientStops>
<GradientStop Color="LightBlue" Offset="1" />
<GradientStop Color="White" Offset="0" />
</RadialGradientBrush.GradientStops>
</RadialGradientBrush>
</Setter.Value>
</Setter>
<Setter Property="ToolTip.Template">
<Setter.Value>
<ControlTemplate>
<Grid Background="{TemplateBinding Property=Control.Background}">
<ContentPresenter Content="{TemplateBinding
Property=ContentControl.Content}"
Margin="{TemplateBinding
Property=Control.Padding}"/>
</Grid>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>

Lo and behold: a nice gradient to all my tooltips! But... why does the
tooltip still have a shadow? I thought that Control Template replaced all
layout...

Erno