template associated with style plugin, and then customized for particular view: views does not find template

I am not sure if this is a bug, or if I am doing something wrong.

I have a style plugin, 'mystyle'. And I created a view, 'myview', with style set to 'mystyle'.

Here is the declaration of 'mystyle' in hook_view_plugins:

function mymodule_views_plugins() {
  $plugins = array(
    'module' => 'mymodule', 
    'style' => array(
      'mystyle' => array(
        'title' => t('My Style'),
        'handler' => 'mymodule_views_plugin_mystyle', 
        'theme' => 'mymodule_views_plugin_mystyle_template',
        'uses fields' => TRUE,
        'uses row plugin' => FALSE, 
        'uses options' => TRUE, 
        'uses grouping' => FALSE,
        'type' => 'normal',
        'even empty' => FALSE, 
      ),
    )
  );
  return $plugins;
}

I have the following files in mymodule/views:

handler:
mymodule_views_plugin_mystyle.inc

template associated with this style:
mymodule-views-plugin-mystyle-template.tpl.php

template associated with this style, and customized for the view 'myview':
mymodule-views-plugin-mystyle-template--myview.tpl.php

My problem:
Views is using the first, less specific, template (mymodule-views-plugin-mystyle-template.tpl.php) to display this view.

When I edit 'myview' and click on "theme information", I see both templates listed under "style output":
mymodule-views-plugin-mystyle-template.tpl.php
mymodule-views-plugin-mystyle-template--myview.tpl.php

The first, less specific, template is in bold. If I understand correctly, this means that views found the first template but did not find the second.

I have tried rescanning, but that does not help. I have also tried deleting the cache.

Should this work? What do I need to do to get views to find (and apply) the more specific template?