What seemed to work for me is unchecking the “newly registered users can post” box and in wp-admin/menu.php, change the user levels to what suits your needs. As an example:
$menu[0] = array(__('Dashboard'), 0, 'index.php');
$menu[5] = array(__('Write'), 5, 'post.php');
$menu[10] = array(__('Manage'), 5, 'edit.php');
$menu[20] = array(__('Links'), 5, 'link-manager.php');
$menu[25] = array(__('Presentation'), 8, 'themes.php');
$menu[30] = array(__('Plugins'), 8, 'plugins.php');
$menu[35] = array(__('Users'), 0, 'profile.php');
$menu[40] = array(__('Options'), 6, 'options-general.php');
if ( get_option('use_fileupload') )
$menu[45] = array(__('Upload'), get_settings('fileupload_minlevel'), 'upload.php');
$submenu['post.php'][5] = array(__('Write Post'), 5, 'post.php');
$submenu['post.php'][10] = array(__('Write Page'), 5, 'page-new.php');
$submenu['edit.php'][5] = array(__('Posts'), 5, 'edit.php');
$submenu['edit.php'][10] = array(__('Pages'), 5, 'edit-pages.php');
$submenu['edit.php'][15] = array(__('Categories'), 5, 'categories.php');
$submenu['edit.php'][20] = array(__('Comments'), 5, 'edit-comments.php');
$awaiting_mod = $wpdb->get_var("SELECT COUNT(*) FROM $wpdb->comments WHERE comment_approved = '0'");
$submenu['edit.php'][25] = array(sprintf(__("Awaiting Moderation (%s)"), $awaiting_mod), 5, 'moderation.php');
$submenu['edit.php'][30] = array(__('Files'), 8, 'templates.php');
$submenu['link-manager.php'][5] = array(__('Manage Links'), 5, 'link-manager.php');
$submenu['link-manager.php'][10] = array(__('Add Link'), 5, 'link-add.php');
$submenu['link-manager.php'][15] = array(__('Link Categories'), 5, 'link-categories.php');
$submenu['link-manager.php'][20] = array(__('Import Links'), 5, 'link-import.php');
$submenu['profile.php'][5] = array(__('Your Profile'), 0, 'profile.php');
$submenu['profile.php'][10] = array(__('Authors & Users'), 5, 'users.php');
$submenu['options-general.php'][5] = array(__('General'), 6, 'options-general.php');
$submenu['options-general.php'][10] = array(__('Writing'), 6, 'options-writing.php');
$submenu['options-general.php'][15] = array(__('Reading'), 6, 'options-reading.php');
$submenu['options-general.php'][20] = array(__('Discussion'), 6, 'options-discussion.php');
$submenu['options-general.php'][25] = array(__('Permalinks'), 6, 'options-permalink.php');
$submenu['options-general.php'][30] = array(__('Miscellaneous'), 6, 'options-misc.php');
$submenu['plugins.php'][5] = array(__('Plugins'), 8, 'plugins.php');
$submenu['plugins.php'][10] = array(__('Plugin Editor'), 8, 'plugin-editor.php');
$submenu['themes.php'][5] = array(__('Themes'), 8, 'themes.php');
$submenu['themes.php'][10] = array(__('Theme Editor'), 8, 'theme-editor.php');