The previously derived characteristic equation of RO in Li, 2010 [8] is used to describe single- or multi-stage ROs with/without an energy recovery device (ERD). Analysis is made at both the theoretical limit (with analytical solutions provided if possible) and practical conditions (using constrained nonlinear optimization). It is shown that reducing specific energy consumption (SEC) normalized by feed osmotic pressure, or NSEC in ROs can be pursued using one or more of the following three independent methods: (1) increasing a dimensionless group gamma=A(total)L(p)Delta pi(0)/Q(f), (2) increasing number of stages, and (3) using an ERD. When gamma increases, the feed rate is adversely affected and the NSEC reduces but flattens out eventually. Using more stages not only reduces NSEC but also improves water recovery. However, The NSEC flattens out when the number of stages increases and ROs with more than five stages are not recommended. Close to the thermodynamic limit where gamma is sufficiently large, the NSEC of ROs up to five stages approaches 4, 3.60, 3.45, 3.38 and 3.33 respectively. The ERD can significantly reduce the NSEC, theoretically to 1, while the corresponding recovery approaches zero. The NSEC becomes larger when the required water recovery increases. It is found that a combination of all three methods can significantly reduce the NSEC while maintaining a high recovery and a reasonable feed or permeate rate. An NSEC around 2.5-2.8 with an 80% water recovery may be possible using 3-5 RO stages and an ERD of 90% efficiency operated at a gamma about 3-5 (or Q(f)=0.2-0.3 A(total)L(p)Delta pi(0)). (C) 2011 Elsevier B.V. All rights reserved.