How to override expanded menu setting

I have a site with a horizontal menu with mouse over effects showing all multi sublevels according to the expanded menu setting.

However I would like to show all submenues in a block showing ONLY current level menu items with an icon indicating possible deeper levels. Take this example below:

I have a menu tree that looks like this with mouse over in my horizontal bar:

Menu 1
- Menu 1.1
- - Menu 1.1.1
- Menu 1.2
- - Menu 1.2.1
- - Menu 1.2.2
- Menu 1.3
- - Menu 1.3.1
- - Menu 1.3.2
- - Menu 1.3.3
Menu 2
(...)

But when showing this menu tree in my vertical Menu Block I only want to show this:

- Menu 1.1
- Menu 1.2
- - **Menu 1.2.1** <-this is the current page being shown
- - Menu 1.2.2
- Menu 1.3

Is this feature possible, and if so how can I make it happen?

Regards,

Nyborg