Alternate Templates

I’m using a heavily modified theme that bears little resemblance to my starting point. The theme I’m using has a format of header-content-sidebar-footer.

However, I need some of my pages (and only specific pages) to display as header-content-footer, because the content is wider on these pages and won’t have room for a sidebar.

I think an alternate page template is my answer, but I’m not sure how I will assign the alternate templates specific pages? I could hard code a page to look like what I want, with or without the includes, but I’m not sure where I create the alternate template …