LetRbe a Krull domain with finite divisor class group Cl(R).We coinsider possible values of ρ(R), the elasticity of factorizations ofR. We first determine an upper bound on ρ(R) based on the distribution of height-one prime ideals in Cl(R) and characterize when his upper bound is attained. We concentrate on the case, wherepis a prime, and determine further bounds on ρ(R) whenk=1 (i.e., Cl(R= Zp). Unlike a related analysis for the cross number of Zpk, we show that the elasticities of such domains do not take on a complete set of hypothesized values.