V2 MIN = 1.2 X Vs or 1.1 X Vmca, whichever is the higher. Utilised as the lowest V2 allowed, and useful for short field operations, or Takeoff at less than maximum weights for the runway, with the 2nd segment OEI gradient suffering as a result of being at less than "Best Gradient Speed" (Vmd for jets).
Increased Speed V2 = A process of optimisation of 2nd segment OEI gradient generally up to Vmd (for jets) but no upper limit is specified. Field performance suffers as a result of the use of "Increased Speed V2", and therefore it's application is useful only on longer runways. Although no upper limit is specified by the regulations, it is usually approximately 1.4 X Vs at the highest.
A fully optimised Airport Analysis may choose a speed between V2 MIN and the optimum OEI best gradient speed, an equal trade-off between Field and Obstacle performance. Leave that one to computerised RTOWs, too hard for humans with sharp pencils.
Old Smokey