For certain cryptography applications, including identity based encryption schemes [1] and short signatures [2], it is important to have simple abelian varieties with security parameters that are neither too small nor too large. Simple supersingular abelian varieties are natural candidates for these applications. This paper gives improvements on the upper bounds of Galbraith [6] for the security parameters of simple supersingular abelian varieties, and constructs several families of curves whose jacobians achieve these upper bounds. 1