I imagine the tandem breakers you're talking about are the twin style type. 2-15, or 20A type. The panel has to be designed to accept them. The diagram (on the panel door) will let you know. Another give away would be the bus would be notched at these locations. If not, the full size must be used. I'm refering to Murray,
and some Croise Hinds. I may be wrong in the spelling. I would hate to be the guy that worked in the panel last and created a Fire Hazard.