We design, fabricate, and test photonic crystal heterostructure cavity lasers in the InP material system. A heterostructure cavity is formed by interfacing two different photonic crystals such that a dispersion maximum of the inner lattice lies within the band gap of the surrounding lattice. Feedback to slow light modes of the central region results in a lower threshold and single mode operation. The use of a kagome lattice as the inner defect area increases the semiconductor volume as well as the modal overlap with the gain material. We use a simulation technique to verify experimentally observed single mode operation as well as to quantify the effects of the heterostructure cavity formation.