Templated ComboBox fires SelectionChanged twice

I have a combobox that I styled to have another combo box inside it (to add
some visual functionality). However, because I have two combos (the logical
and the visual) that are two-way bound to one another, when I make a
selection, the SelectionChanged event fires twice. I'm not sure how to mask
the event when it's triggered via a binding outside taking my custom
template out altogether, which isn't an option:
<Style x:Key="PickList"
TargetType="{x:Type ComboBox}">
<Setter Property="MinWidth"
Value="150"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type ComboBox}">
<Grid>
<Grid.ColumnDefinitions>
<ColumnDefinition Width="Auto"/>
<ColumnDefinition Width="19"/>
</Grid.ColumnDefinitions>

<ComboBox Grid.ColumnSpan="2"
ItemsSource="{TemplateBinding
ItemsSource}"
ItemTemplate="{TemplateBinding
ItemTemplate}"
SelectedItem="{Binding
RelativeSource={x:Static RelativeSource.TemplatedParent}, Path=SelectedItem,
Mode=TwoWay}"
MinHeight="{TemplateBinding
MinHeight}"
MinWidth="{TemplateBinding
MinWidth}"/>
<Border Margin="2,2,2,1"
I****TestVisible="False">
<StackPanel Name="SelectLabel"
Visibility="Hidden"
Orientation="Horizontal"
HorizontalAlignment="Center"
Margin="{TemplateBinding
Control.Padding}">
<TextBlock Style="{StaticResource
PickListNullItem}"
Text="Select a "/>
<TextBlock Style="{StaticResource
PickListNullItem}"
Text="{TemplateBinding
Name}"/>
</StackPanel>
</Border>
</Grid>
<ControlTemplate.Triggers>
<Trigger Property="SelectedItem"
Value="{x:Null}">
<Setter Property="Visibility"
Value="Visible"
TargetName="SelectLabel"/>
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>