how to delete widgets default HTML

I created a widget section in the theme I created. When I drag widgets to the new area and look at the page, wordpress puts in all these div’s with the class name “textwidget” in there and its messing up my layout and css. Can I get it so the widgets do not have those default div’s and class names?

I figure the only HTML the widgets should have are the ones I specify in the new function, (before widget, after widget, before title, after title).

Any help would be great.