Flow cardinality estimation is the problem of estimating the number of distinct elements in a data flow, often with a stringent memory constraint. It has wide applications in network traffic measurement and in database systems. The virtual HyperLogLog (vHLL) algorithm proposed by Xiao, Chen, Chen and Ling  estimates the cardinalities of a large number of flows with a compact memory. This paper explores two new estimation algorithms based on the same compact memory used in . Firstly, we propose and investigate a family of estimators that generalizes the original vHLL estimator. Secondly, we derive an approximate maximum-likelihood estimator. Empirical evidence suggests the near-optimality of the original vHLL estimator for per-flow estimation, analogous to the near-optimality of the HyperLogLog estimator for single-flow estimation. We also propose weighted square error, a single-value metric that quantifies the performance of an estimator.