On one of the Russian web sites there is an interview with Rafail Murtazin, deputy head of ballistics department of the Energia corporation, who is described as the developer of the expedited rendezvous scheme. In brief, they have achieved this as follows (I apologize for possibly incorrect terms, please feel free to edit).
Firstly, the ISS orbit is adjusted in advance to ensure that on the launch date the phase angle between the two crafts is within 30-35 degrees.
Secondly, Soyuz makes its first orbit transfer on the very first orbit, using theoretical orbit parameters computed before launch. This is in contrast with the two-day rendezvous scheme, where they measure actual orbital parameters before the transfer, which takes them two extra orbits.
At the bottom of the interview page is a link to the presentation on the topic (PowerPoint, in Russian) Murtazin gave at a conference at the Bauman State Technical University in 2013; it has all sorts of diagrams showing in detail the entire launch and rendezvous process.