Several naturally distributed negotiation/cooperation problems with privacy requirements can be modeled within the distributed constraint satisfaction framework, where the constraints are secrets of the participants. Most of the existing techniques aim at various tradeoffs between complexity and privacy guarantees, while others aim to maximize privacy first [12, 7, 3, 4, 11]. In [7] we introduced a first technique allowing agents to solve distributed constraint problems (DisCSPs), without revealing anything and without trusting each other or some server. The technique we propose now is a dm times improvement for m variables of domain size d. On the negative side, the fastest versions of the new technique require storing of O(d{m}) big integers. From a practical point of view, we improve the privacy with which these problems can be solved, and improve the efficiency with which [n-1/2]-privacy can be achieved, while it remains inapplicable for larger problems. The technique of [7] has a simple extension to optimization for distributed weighted CSPs. However, that obvious extension leaks to everybody sensitive information concerning the quality of the computed solution. We found a way to avoid this leak, which constitutes another contribution of this paper.