The US health insurance industry is highly concentrated, and health insurance premiums are high and rising rapidly. Policymakers have focused on the possible link between the two, leading to ACA provisions to increase insurer competition. However, while market power may enable insurers to include higher profit margins in their premiums, it may also result in stronger bargaining leverage with hospitals to negotiate lower payment rates to partially offset these higher premiums. We empirically examine the relationship between employer-sponsored fully-insured health insurance premiums and the level of concentration in local insurer and hospital markets using the nationally-representative 2006-2011 KFF/HRET Employer Health Benefits Survey. We exploit a unique feature of employer-sponsored insurance, in which self-insured employers purchase only administrative services from managed care organizations, to disentangle these different effects on insurer concentration by constructing one concentration measure representing fully-insured plans' transactions with employers and the other concentration measure representing insurers' bargaining with hospitals. As expected, we find that premiums are indeed higher for plans sold in markets with higher levels of concentration relevant to insurer transactions with employers, lower for plans in markets with higher levels of insurer concentration relevant to insurer bargaining with hospitals, and higher for plans in markets with higher levels of hospital market concentration.