There has been much discussion in Israel about modifying the draft. The main problem is a surplus in manpower. With the country's population approaching seven million, there simply are more young people than the army needs to carry out all its responsibilities cost-effectively. Unofficially, you can already avoid military service rather easily. In a sense, nobody should protest the charedi refusal to serve, because the army doesn't need them. What motivates anti-charedi protest, as well as the broad opposition to switching to a volunteer army, is the justified feeling that the army must include everyone for fairness and for socialization.
An obvious suggestion is to decrease the length of service. But for every problem this would solve, another would be created. Soldiers who serve a shorter period spend more of their service in training and thus are more expensive. And while there are too many soldiers overall, there is still a shortage in combat and professional positions. These training-intensive positions, as well as leadership positions, would still require an extended period of service. Shortening the basic period of service would further discourage people from choosing positions which the army really needs.
If the draft cannot be made voluntary and service cannot be shortened, the only option is to categorically exclude certain groups. There are two main concerns in such exclusion: fairness and efficacy. A lottery system would be fair, but not efficacious, because many of the best candidates would not be selected. Excluding the charedim is unfair, but efficacious - due to the political and social difficulty of including them, and because they might not make good soldiers anyway. Perhaps any system which preferences certain groups for practical reasons will necessarily be unfair. What is left is to aim for a system which maximizes gain and minimizes unfairness.
I think the best selection method is to draft all men for a full three years, but to excuse women from the draft. This implies discrimination on an individual level. But unlike all other possible selection methods, on a broad level it is perfectly equitable. Since every family on average contains an equal number of men and women, all social, economic, and ethnic groups would be treated equally. Furthermore, because families normally share resources among their members, the time and money burden would in fact be spread among every member of society. Men already serve longer than women and dominate combat units, so the areas of current shortage would not lose out. But the overall pool of manpower would be much smaller, and the army would no longer have to find work for many soldiers it does not need.
This approach also has several incidental but significant benefits for Israeli society. With women marrying and entering the workforce two years earlier, the country would gain economically, women would come closer to professional equality with men, and the birthrate in population groups loyal to the state would rise. Removing women from the army is desirable from a religious perspective (or from the perspective of appeasing the religious), both intrinsically and due to the freedom of behavior common in the current, mixed army. Such a removal could be paired with a large-scale induction of charedi men, resulting in perhaps an acceptable trade-off from the charedi perspective, along with the equal sharing of the defense burden among the entire Jewish population.
Weaknesses of the plan include the large gap in time commitment between men and women, and the loss by women of the socialization obtained in the army. These concerns could be addressed by requiring a year of national service from women, which might conceivably be extended to Arabs as well. Also, while women would presumably still be able to volunteer for military service, those few who do would probably have a harder time than at present. But this seems a small price to pay, when all other women would be entirely released from their current obligations.
There are currently demands in Israel to reduce the army's size, to privatize non-essential army services, to draft all populations on an equal basis, to crack down on draft and miluim evaders, to make the army environment more friendly to the religious, to increase enlistment in elite units, to decrease the economic burden caused by extended service, and so on. Unfortunately, many of these demands work at cross-purposes and might seem to be mutually exclusive. But almost all of them could be be reconciled by drafting all Jewish men, but only men. No other plan would come close to helping the areas we would like the army to improve in. Such a plan would indeed have novel side effects, but the probably scope of gain certainly makes them worth bearing.