Odd Border effect on ItemsControl with ScrollViewer in ControlTemplate

Question

I've got an ItemsControl (in a DockPanel with other stuff) which has a ControlTemplate to provide a ScrollViewer because the items won't fit on the screen. With the given config, I get a strange double-border top and bottom. It looks like a grey line above the top line and another below the bottom line. The sides are unaffected. I get the same effect if I remove the BorderBrush and BorderThickness from the ItemsControl and specify them explicitly on the ScrollViewer. How do I make it go away?

<ItemsControl DockPanel.Dock="Bottom" Margin="0" Name="uxPropertiesRegion"
              MinWidth="50" Height="100" MinHeight="50" 
              BorderBrush="Black" BorderThickness="1"
              ClipToBounds="True"
              cal:RegionManager.RegionName="{x:Static local:ADRegionNames.CentreBottomRegion}"
              Visibility="{Binding Path=Items.Count,
                                   ElementName=uxPropertiesRegion,
                                   Converter={StaticResource countToVis} }">
    <ItemsControl.Template>
        <ControlTemplate>
            <Border Background="{TemplateBinding Background}"
                    BorderBrush="{TemplateBinding BorderBrush}"
                    BorderThickness="{TemplateBinding BorderThickness}">
                <ScrollViewer x:Name="ScrollViewer" 
                              Padding="{TemplateBinding Padding}">
                    <ItemsPresenter />
                </ScrollViewer>
            </Border>
        </ControlTemplate>
    </ItemsControl.Template>
</ItemsControl>