This article examines a model of competition between two types of health insurer: Health Maintenance Organizations (HMOs) and nonintegrated insurers. HMOs vertically integrate health care providers and pay them at a competitive price, while nonintegrated health insurers work as indemnity plans and pay the health care providers freely chosen by policyholders at a wholesale price. Such difference is referred to as an input price effect which, at first glance, favors HMOs. Moreover, we assume that policyholders place a positive value on the provider diversity supplied by their health insurance plan and that this value increases with the probability of disease. Due to the restricted choice of health care providers in HMOs a risk segmentation occurs: policyholders who choose nonintegrated health insurers are characterized by higher risk, which also tends to favor HMOs. Our equilibrium analysis reveals that the equilibrium allocation only depends on the number of HMOs in the case of exclusivity contracts between HMOs and providers. Surprisingly, our model shows that the interplay between risk segmentation and input price effects may generate ambiguous results. More precisely, we reveal that vertical integration in health insurance markets may decrease health insurers' premiums.