Nearest-neighbor search over time series has received vast research attention as a basic data mining task. Still, none of the hitherto proposed methods scales well with increasing time-series length. This is due to the fact that all methods provide an one-off pruning capacity only. In particular, traditional methods utilize an index to search in a reduced-dimensionality feature space; however, for high time-series length, search with such an index yields many false hits that need to be eliminated by accessing the full records. An attempt to reduce false hits by indexing more features exacerbates the curse of dimensionality, and vice versa. A recently proposed alternative, iSAX, uses symbolic approximate representations accessed by a simple file-system directory as an index. Still, iSAX also encounters false hits, which are again eliminated by accessing records in full: once a false hit is generated by the index, there is no second chance to prune it; thus, the pruning capacity iSAX provides is also one-off. This paper proposes an alternative approach to time series kNN search, following a nontraditional pruning style. Instead of navigating through candidate records via an index, we access their features, obtained by a multi-resolution transform, in a stepwise sequential-scan manner, one level of resolution at a time, over a vertical representation. Most candidates are progressively eliminated after a few of their terms are accessed, using pre-computed information and an unprecedentedly tight double-bounding scheme, involving not only lower, but also upper distance bounds. Our experimental study with large, high-length time-series data confirms the advantage of our approach over both the current state-of-the-art method, iSAX, and classical index-based methods.