How to set up multiple items in JList using setselectedvalue?

I have a JList that is dynamically populated by adding to the underlying listmodel Now, if I have three strings, I know and I know its value

for(i=0;i<3;i++){
    jList.setSelectedValue(obj[i],true);//true is for shouldScroll or not
}

Only the last item seems to be selected... If this cannot be done, I must choose from the basic model settings. How should I do it?

Also note that JList has a selection mode:

jList.setSelectionMode(ListSelectionModel.MULTIPLE_INTERVAL_SELECTION);

Thank you in advance

Solution

Although stanislasv answer works perfectly, I'd rather avoid adding one selection interval to another Instead, you should prefer to call the listselectionmodel#setselectioninterval (int, int) method associated with JList like this:

jList.getSelectionModel().setSelectionInterval(0,3)

If you want list selections to be disjoint, you must also write your own listselectionmodel