The vehicle routing problem with stochastic demands (VRPSD) consists of designing transportation routes of minimal expected cost to satisfy a set of customers with random demands of known probability distribution. This paper tackles a generalization of the VRPSD known as the multicompartment VRPSD (MC-VRPSD), a problem in which each customer demands several products that, because of incompatibility constraints, must be loaded in independent vehicle compartments. To solve the problem, we propose three simple and effective constructive heuristics based on a stochastic programming with recourse formulation. One of the heuristics is an extension to the multicompartment scenario of a savings-based algorithm for the VRPSD; the other two are different versions of a novel look-ahead heuristic that follows a route-first, cluster-second approach. In addition, to enhance the performance of the heuristics these are coupled with a post-optimization procedure based on the classical 2-Opt heuristic. The three algorithms were tested on instances of up to 200 customers from the MC-VRPSD and VRPSD literature. The proposed heuristics unveiled 26 and 12 new best known solutions for a set of 180 MC-VRPSD problems and a 40-instance testbed for the VRPSD, respectively.