We study a modification of the Threshold ALOHA policy that we refer to as Mini Slotted Threshold ALOHA (MiSTA). In MiSTA, as in Threshold ALOHA, sources with age of information (AoI) below a certain threshold F are inactive. In addition, each time slot is preceded by a mini slot during which active sources test the channel with a certain probability, tau(1). Colliding transmitters independently decide to continue transmission with probability tau(2) < tau(1) during the rest of the slot. Analyzing the steady state distribution of the number of active sources in the large network limit, it is shown that MiSTA probabilistically converges to a "thinned" Threshold ALOHA. With optimal selection of the parameters, the AoI scales with the network size, n, as 0.9641n, in contrast to the 1.4169n achieved by Threshold ALOHA. In addition to achieving this reduction in age, MiSTA also increases the throughput to approximately 53%, which is a significant improvement over the 37% achievable by Threshold ALOHA and regular Slotted ALOHA.