The proliferation of fast, dense, byte-addressable nonvolatile memory suggests that data might be kept in pointer-rich "in-memory" format across program runs and even process and system crashes. For full generality, such data requires dynamic memory allocation, and while the allocator could in principle "rolled into" each data structure, it is desirable to make it a separate abstraction. Toward this end, we introduce recoverability, a correctness criterion for persistent allocators, together with a nonblocking allocator, Ralloc, that satisfies this criterion. Ralloc is based on the LRMalloc of Leite and Rocha, with three key innovations. First, we persist just enough information during normal operation to permit correct reconstruction of the heap after a full-system crash. Our reconstruction mechanism performs garbage collection (GC) to identify and remedy any failure-induced memory leaks. Second, we introduce the notion of filter functions, which identify the locations of pointers within persistent blocks to mitigate the limitations of conservative GC. Third, to allow persistent regions to be mapped at an arbitrary address, we employ position-independent (offset-based) pointers for both data and metadata. Experiments show Ralloc to be performance-competitive with both Makalu, the state-of-the-art lock-based persistent allocator, and such transient allocators as LRMalloc and JEMalloc. In particular, reliance on GC and offline metadata reconstruction allows Ralloc to pay almost nothing for persistence during normal operation.