This paper presents two novel ideas of improving the Machine Translation (MT) quality by applying the word-level quality prediction for the second pass of decoding. In this manner, the word scores estimated by word confidence estimation systems help to reconsider the MT hypotheses for selecting a better candidate rather than accepting the current sub-optimal one. In the first attempt, the selection scope is limited to the MT N-best list, in which our proposed re-ranking features are combined with those of the decoder for re-scoring. Then, the search space is enlarged over the entire search graph, storing many more hypotheses generated during the first pass of decoding. Over all paths containing words of the N-best list, we propose an algorithm to strengthen or weaken them depending on the estimated word quality. In both methods, the highest score candidate after the search becomes the official translation. The results obtained show that both approaches advance the MT quality over the one-pass baseline, and the search graph re-decoding achieves more gains (in BLEU score) than N-best List Re-ranking method.