Cutting Circles in Thick Card

Working on a model where I've laminated paper to a cereal box backer. It has many circles of different sizes, all in the small range. Am having real difficulty cutting them out and am also burning through X-acto blades at an alarming rate. Have read through all the applicable threads I can find and am still somewhat in the dark. What do you use to cut out small circles in thick cardboard? Punches, lots of X-acto blades? Alien technology? (Still practicing circle cutting and blade sharpening. Not there yet but am learning)