Network management protocols often require timely and meaningful insight about per flow network traffic. This paper introduces Randomized Admission Policy (RAP) -a novel algorithm for the frequency, top-k, and byte volume estimation problems, which are fundamental in network monitoring. We demonstrate space reductions compared to the alternatives, for the frequency estimation problem, by a factor of up to 32 on real packet traces and up to 128 on heavy-tailed workloads. For top-k identification, RAP exhibits memory savings by a factor of between 4 and 64 depending on the workloads' skewness. These empirical results are backed by formal analysis, indicating the asymptotic space improvement of our probabilistic admission approach. In Addition, we present d-way RAP, a hardware friendly variant of RAP that empirically maintains its space and accuracy benefits.