We consider the problem of distributed admission control without knowledge of the capacity region in single-hop wireless networks, for flows that require a pre-specified bandwidth from the network. We present an optimization framework that allows us to design a scheduler and resource allocator, and by properly choosing a suitable utility function in the resource allocator, we prove that existing flows can be served with a prespecified bandwidth, while the link requesting admission can determine the largest rate that it can get such that it does not interfere with the allocation to the existing flows.