Data used in recreation demand modeling are characterized by the facts that trip frequencies are non-negative integers and that consumers are often faced with alternative destinations. This paper considers these features by estimating a multivariate recreation demand model that accounts for trip frequency and choice among alternative recreation sites using a mixed multinomial-Poisson hurdle distribution. The specification of the Poisson hurdle distribution at the aggregate level accounts for participation and trip frequency, and avoids the restrictive mean-variance property of the basic Poisson model. The model is estimated using data from Bighorn sheep hunters in Alberta, Canada. Simulation results suggest that changing price and quality variables cause substitution among sites. The welfare implications of changes in these variables are also examined.