To provide quick responses to users, Internet companies rely on online data systems able to answer queries in milliseconds. These systems employ complementary overload management techniques to ensure they provide a continued, acceptable service through-out traffic surges, where 'acceptable' partly means that serviced queries meet or track closely their response time objectives. Thus, in this paper we present Bouncer, an admission control policy aimed to keep admitted queries under or near their service level objectives (SLOs) on percentile response times. It computes inexpensive estimates of percentile response times for every incoming query and compares the estimates against the objective values to decide whether to accept or reject the query. Bouncer allows assigning separate SLOs to different classes of queries in the workload, implements early rejections to let clients react promptly and to help data systems avoid doing useless work, and complements other load shedding policies that guard systems from exceeding their capacity. Moreover, we propose two starvation avoidance strategies that supplement Bouncer's basic formulation and prevent query types from receiving no service (starving). We evaluate Bouncer and its starvation-avoiding variants against other policies in simulation and on a production-grade in-memory distributed graph database. Our results show that Bouncer and its variants allow admitted queries to meet or stay close to the SLOs when the other policies do not. They also report fewer overall rejections, a small overhead, and with the given latency SLOs, they let the system reach high utilization. In addition, we observe that the proposed strategies can stop query starvation, but at the expense of a modest increase in overall rejections and causing SLO violations for serviced requests.