In the video A Concept Design for C++ and the related paper Design of Concept Libraries for C++ Bjarne Stroustrup and Andrew Sutton describe how they're going avoid the problems that lead to concepts getting voted out of C++11. In a nutshell they seem to be focusing on the simplest thing that could possibly work for STL (C++'s Standard Template Library).
C++ does not provide facilities for directly expressing what a function template requires of its set of parameters. This is a problem that manifests itself as poor error messages, obscure bugs, lack of proper overloading, poor specification of interfaces, and maintenance problems.
Many have tried to remedy this (in many languages) by adding sets of requirements, commonly known as "concepts." Many of these efforts, notably the C++0x concept design, have run into trouble by focusing on the design of language features.
This talk presents the results of an effort to first focus on the design of concepts and their use; Only secondarily, we look at the design of language features to support the resulting concepts. We describe the problem, our approach to a solution, give examples of concepts for the STL algorithms and containers, and finally show an initial design of language features. We also show how we use a library implementation to test our design.
So far, this effort has involved more than a dozen people, including the father of the STL, Alex Stepanov, but we still consider it research in progress rather than a final design. This design has far fewer concepts than the C++0x design and far simpler language support. The design is mathematically well founded and contains extensive semantic specifications (axioms).