In this paper, we revisit the classic CountSketch method, which is a sparse, random projection that transforms a (high-dimensional) Euclidean vector v to a vector of dimension (2t - 1)s, where t, s > 0 are integer parameters. It is known that a CountSketch allows estimating coordinates of v with variance bounded by parallel to v parallel to/s. For t > 1, the estimator takes the median of 2t - 1 independent estimates, and the probability that the estimate is off by more than 2 parallel to v parallel to/root s is exponentially small in t. This suggests choosing t to be logarithmic in a desired inverse failure probability. However, implementations of CountSketch often use a small, constant t. Previous work only predicts a constant factor improvement in this setting. Our main contribution is a new analysis of CountSketch, showing an improvement in variance to O(min{parallel to v parallel to, parallel to v parallel to/s}) when t > 1. That is, the variance decreases proportionally to s, asymptotically for large enough s.