How do I stretch the contents of a HeaderedContentControl?

I have a HeaderedContentControl that contains a TreeView.

    <HeaderedContentControl Header="Steps" HorizontalAlignment="Stretch" VerticalAlignment="Stretch">
        <TreeView Name="WizardSteps" ItemsSource="{Binding WizardSteps}" HorizontalAlignment="Stretch" VerticalAlignment="Stretch">
            <!-- Hierarchical data templates here -->
        </TreeView>
    </HeaderedContentControl>

Although the HeaderedContentControl stretches to fill the area inside its parent grid, my TreeView control only occupies a small portion of the space available.

How do I get my TreeView to expand to fill the content area of my HeaderedContentControl?