Big Harvest

Today, I was cleaning out my shared alley bed and came across a few carrots from last year. They were all still tiny, despite having been in the ground for almost a year. I'm going to have to investigate what kind of soil carrots like. The soil is loose and rich, so I get big tops and small carrots. Maybe the soil has too much nitrogen. Does anyone out there know how I can amend the soil to get bigger carrots?