There are a few different ways that you can keep snickerdoodles from spreading. One way is to make sure that you use the correct amount of flour when you are making the dough. Too much flour will cause the dough to be too dry and this will cause the cookies to spread. Another way to prevent spreading is to chill the dough before baking. This will help to firm up the butter and prevent it from melting too quickly when it hits the hot oven. Finally, do not over-bake your cookies! Cookies that are baked for too long will become crisp and this will cause them to spread as well.