WPF - How do I default the Visibility of a databound Textblock?

This Textblock, defined below, shows when the window first loads because it has no Datacontext (and hence the converter code is not run) until an item has been selected from another control e.g. TreeView.

<TextBlock
   Name="tbkDocumentNotFound" 
   Style="{StaticResource StandardText}"
   Margin="4,4,2,0" 
   TextWrapping="Wrap"                                    
   Visibility="{Binding Path=IsDownloaded, Converter={StaticResource docNotFoundVisibilityConverter}, Mode=TwoWay}"
   Text="The document could not be found.">
</TextBlock>

So how do I stop the it from appearing when it has no DataContext?

Thanks.