We present an assessment of the performance of a new on-line bin packing algorithm, which can interpolate smoothly from the Next Fit to Best Fit algorithms, as well as encompassing a new class of heuristic which packs multiple blocks at once. The performance of this novel O(n) on-line algorithm can be better than that of the Best Fit algorithm. The new algorithm runs about an order of magnitude slower than Next Fit, and about two orders of magnitude faster than Best Fit, on large sample problems. It can be tuned for optimality in performance by adjusting parameters which set its working memory usage, and exhibits a sharp threshold in this optimal parameter space as time constraint is varied. These optimality concerns provide a testbed for the investigation of the value of memory and attention-like properties to algorithms.