Ergodic interference alignment, as introduced by Nazer et al (NGJV), is a technique that allows high-rate communication in n-user interference networks with fast fading. It works by splitting communication across a pair of fading matrices. However, it comes with the overhead of a long time delay until matchable matrices occur: the delay is q^n^2 for field size q. In this paper, we outline two new families of schemes, called JAP and JAP-B, that reduce the expected delay, sometimes at the cost of a reduction in rate from the NGJV scheme. In particular, we give examples of good schemes for networks with few users, and show that in large n-user networks, the delay scales like q^T, where T is quadratic in n for a constant per-user rate and T is constant for a constant sum-rate. We also show that half the single-user rate can be achieved while reducing NGJV's delay from q^n^2 to q^(n-1)(n-2). This extended version includes complete proofs and more details of good schemes for small n. ; Comment: Extended version of a paper presented at the 2012 International Symposium on Information Theory. 7 pages, 1 figure