Existing robotic systems have a clear tension between generality and precision. Deployed solutions for robotic manipulation tend to fall into the paradigm of one robot solving a single task, lacking precise generalization, i.e., the ability to solve many tasks without compromising on precision. This paper explores solutions for precise and general pick-and-place. In precise pick-and-place, i.e. kitting, the robot transforms an unstructured arrangement of objects into an organized arrangement, which can facilitate further manipulation. We propose simPLE (simulation to Pick Localize and PLacE) as a solution to precise pick-and-place. simPLE learns to pick, regrasp and place objects precisely, given only the object CAD model and no prior experience. We develop three main components: task-aware grasping, visuotactile perception, and regrasp planning. Task-aware grasping computes affordances of grasps that are stable, observable, and favorable to placing. The visuotactile perception model relies on matching real observations against a set of simulated ones through supervised learning. Finally, we compute the desired robot motion by solving a shortest path problem on a graph of hand-to-hand regrasps. On a dual-arm robot equipped with visuotactile sensing, we demonstrate pick-and-place of 15 diverse objects with simPLE. The objects span a wide range of shapes and simPLE achieves successful placements into structured arrangements with 1mm clearance over 90% of the time for 6 objects, and over 80% of the time for 11 objects. Videos are available at http://mcube.mit.edu/research/simPLE.html .