Neighbourhood singleton arc consistency (NSAC) is a type of singleton arc consistency (SAC) in which the subprob- lem formed by variables adjacent to a variable with a singleton domain is made arc consistent. This paper describes two exten- sions to neighbourhood SAC. The first is a generalization from NSAC to k-NSAC, where k is the maximum length of the shortest path between the singleton variable and any variable in the subgraph. The second is an extension of k-NSAC to problems with n-ary constraints, which retains the basic definition of a k-neighbourhood subgraph. To establish such consistencies a suite of algorithms is considered based on various SAC algorithms including SAC-1, SACQ, SAC-SDS, and SAC-3. In analyzing these different algorithms it was found useful to distinguish between and SAC algorithms, based on the complexity of data structures and procedures needed to carry out the task of establishing (N)SAC. Under this classification, SAC-1 and SACQ are light-weight; the other two (and SAC-2) are heavy-weight. It was found that only light-weight algorithms can be readily and effectively transformed into efficient NSAC algorithms. In contrast, because of their specialized procedures, it was necessary to modify heavy-weight algorithms significantly, which also compromised performance. Extensive experimental analysis shows that with a spectrum of neighbourhood consistencies and attendant algorithms, one can finesse the fundamental tradeoff between efficiency and effectiveness across a greater range of problems than with SAC and NSAC algorithms alone. This work serves to enlarge the scope of SAC-based consistency maintenance as well as defining the various niches that light-weight and heavy-weight algorithms are best suited for.